Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Intermediate Algebra
Explain what it mean to factor a polynomial completely.The difference of squares y4625 can be factored as (y225)(y2+25) . But it is not completely factored. What more must be done to completely factor.Of all the factoring methods covered in this chapter (GCF, grouping, undo FOIL, ‘ac’ method, special products) which is the easiest for you? Which is the hardest? Explain your answers.Create three factoring problems that would be good test questions to measure your knowledge of factoring. Show the solutions.Solve: (3m2)(2m+1)=0 .Solve: (4p+3)(4p3)=0 .Solve: 3c2=10c8 .Solve: 2d25d=3 .Solve: 25p2=49 .Solve: 36x2=121 .Solve: (2m+1)(m+3)=12m .Solve: (k+1)(k1)=8 .Solve: 18a230=33a .Solve: 123b=660b2 .Solve: 8x3=24x218x .Solve: 16y2=32y3+2y .For the function f(x)=x22x8 , (a) find x when f(x)=7 (b) Find two points that lie on the graph of the function.For the function f(x)=x28x+3 , (a) find x when f(x)=4 (b) Find two points that lie on the graph of the function.For the function f(x)=2x27x+5 , find (a) the zeros of the function (b) any x-intercepts of the graph of the function (c) any y-intercepts of the graph of the function.For the function f(x)=6x2+13x15 , find (a) the zeros of the function (b) any x-intercepts of the graph of the function (c) any y-intercepts of the graph of the function.The product of two consecutive odd integers is 255. Find the integers.The product of two consecutive odd integers is 483 Find the integers.A rectangular sign has area 30 square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.A rectangular patio has area 180 square feet. The width of the patio is three feet less than the length. Find the length and width of the patio.Justine wants to put a deck in the corner of her backyard in the shape of a right triangle. The length of one side of the deck is 7 feet more than the other side. The hypotenuse is 13. Find the lengths of the two sides of the deck.A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of the other leg. Find the lengths of the hypotenuse and the other leg.Genevieve is going to throw a rock from the top a trail overlooking the ocean. When she throws the rock upward from 160 feet above the ocean, the function h(t)=16t2+48t+160 models the height, h, of the rock above the ocean as a function of time, t. Find: (a) the zeros of this function which tell us when the rock will hit the ocean (b) when the rock will be 160 feet above the ocean. (c) the height of the rock at t=1.5 seconds.Calib is going to throw his lucky penny from his balcony on a cruise ship. When he throws the penny upward from 128 feet above the ground, the function h(t)=16t2+32t+128 models the height, h, of the penny above the ocean as a function of time, t. Find: (a) the zeros of this function which is when the penny will hit the ocean (b) when the penny will be 128 feet above the ocean. (c) the height the penny will be at t=1 seconds which is when the penny will be at its highest point.In the following exercises, solve. 277. (3a10)(2a7)=0In the following exercises, solve. 278. (5b+1)(6b+1)=0In the following exercises, solve. 279. 6m(12m5)=0In the following exercises, solve. 280. 2x(6x3)=0In the following exercises, solve. 281. (2x1)2=0In the following exercises, solve. 282. (3y+5)2=0In the following exercises, solve. 283. 5a226a=24In the following exercises, solve. 284. 4b2+7b=3In the following exercises, solve. 285. 4m2=17m15In the following exercises, solve. 286. n2=56nIn the following exercises, solve. 287. 7a2+14a=7aIn the following exercises, solve. 288. 12b215b=9bIn the following exercises, solve. 289. 49m2=144In the following exercises, solve. 290. 625=x2In the following exercises, solve. 291. 16y2=81In the following exercises, solve. 292. 64p2=225In the following exercises, solve. 293. 121n2=36In the following exercises, solve. 294. 100y2=9In the following exercises, solve. 295. (x+6)(x3)=8In the following exercises, solve. 296. (p5)(p+3)=7In the following exercises, solve. 297. (2x+1)(x3)=4xIn the following exercises, solve. 298. (y3)(y+2)=4yIn the following exercises, solve. 299. (3x2)(x+4)=12xIn the following exercises, solve. 300. (2y3)(3y1)=8yIn the following exercises, solve. 301. 20x260x=45In the following exercises, solve. 302. 3y218y=27In the following exercises, solve. 303. 15x210x=40In the following exercises, solve. 304. 14y277y=35In the following exercises, solve. 305. 18x29=21xIn the following exercises, solve. 306. 16y2+12=32xIn the following exercises, solve. 307. 16p3=24p2+9pIn the following exercises, solve. 308. m32m2=mIn the following exercises, solve. 309. 2x3+72x=24x2In the following exercises, solve. 310. 3y3+48y=24y2In the following exercises, solve. 311. 36x3+24x2=4xIn the following exercises, solve. 312. 2y3+2y2=12yIn the following exercises, solve. 313. For the function, f(x)=x28x+8 , (a) find when f(x)=4 (b) Use this information to find two points that lie on the graph of the function.In the following exercises, solve. 314. For the function, f(x)=x2+11x+20 , (a) find when f(x)=8 (b) Use this information to find two points that lie on the graph of the function.In the following exercises, solve. 315. For the function, f(x)=8x218x+5 , (a) find when f(x)=4 (b) Use this information to find two points that lie on the graph of the function.In the following exercises, solve. 316. For the function, f(x)=18x2+15x10 , (a) find when f(x)=15 (b) Use this information to find two points that lie on the graph of the function.In the following exercises, for each function, find: (a) the zeros of the function (b) the x-intercepts of the graph of the function (c) the y-intercept of the graph of the function. 317. f(x)=9x24In the following exercises, for each function, find: (a) the zeros of the function (b) the x-intercepts of the graph of the function (c) the y-intercept of the graph of the function. 318. f(x)=25x249In the following exercises, for each function, find: (a) the zeros of the function (b) the x-intercepts of the graph of the function (c) the y-intercept of the graph of the function. 319. f(x)=6x27x5In the following exercises, for each function, find: (a) the zeros of the function (b) the x-intercepts of the graph of the function (c) the y-intercept of the graph of the function. 320. f(x)=12x211x+2In the following exercises, solve. 321. The product of two consecutive odd integers is 143. Find the integers.In the following exercises, solve. 322. The product of two consecutive odd integers is 195. Find the integers.In the following exercises, solve. 323. The product of two consecutive even integers is 168. Find the integers.In the following exercises, solve. 324. The product of two consecutive even integers is 288. Find the integers.In the following exercises, solve. 325. The area of a rectangular carpet is 28 square feet. The length is three feet more than the width. Find the length and the width of the carpet.In the following exercises, solve. 326. A rectangular retaining wall has area 15 square feet. The height of the wall is two feet less than its length. Find the height and the length of the wall.In the following exercises, solve. 327. The area of a bulletin board is 55 square feet. The length is four feet less than three times the width. Find the length and the width of the a bulletin board.In the following exercises, solve. 328. A rectangular carport has area 150 square feet. The height of the carport is five feet less than twice its length. Find the height and the length of the carport.In the following exercises, solve. 329. A pennant is shaped like a right triangle, with hypotenuse 10 feet. The length of one side of the pennant is two feet longer than the length of the other side. Find the length of the two sides of the pennant.In the following exercises, solve. 330. A stained glass window is shaped like a right triangle. The hypotenuse is 15 feet. One leg is three more than the other. Find the lengths of the legs.In the following exercises, solve. 331. A reflecting pool is shaped like a right triangle, with one leg along the wall of a building. The hypotenuse is 9 feet longer than the side along the building. The third side is 7 feet longer than the side along the building. Find the lengths of all three sides of the reflecting pool.In the following exercises, solve. 332. A goat enclosure is in the shape of a right triangle. One leg of the enclosure is built against the side of the barn. The other leg is 4 feet more than the leg against the barn. The hypotenuse is 8 feet more than the leg along the barn. Find the three sides of the goat enclosure.In the following exercises, solve. 333. Juli is going to launch a model rocket in her back yard. When she launches the rocket, the function h(t)=16t2+32t models the height, h, of the rocket above the ground as a function of time, t. Find: (a) the zeros of this function which tells us when the rocket will hit the ground. (b) the time the rocket will be 16 feet above the ground.In the following exercises, solve. 334. Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 48 feet above the ground, the function h(t)=16t2+32t+48 models the height, h, of the ball above the ground as a function of time, t. Find: (a) the zeros of this function which tells us when the ball will hit the ground. (b) the time(s) the ball will be 48 feet above the ground. (c) the height the ball will be at t=1 seconds which is when the ball will be at its highest point.Explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic equation?Give an example of a quadratic equation that has a GCF and none of the solutions to the equation is zero.In the following exercises, find the greatest common factor. 337. 12a2b3,15ab2In the following exercises, find the greatest common factor. 338. 12m2n3,42m5n3In the following exercises, find the greatest common factor. 339. 15y3,21y2,30yIn the following exercises, find the greatest common factor. 340. 45x3y2,15x4y,10x5y3In the following exercises, factor the greatest common factor from each polynomial. 341. 35y+84In the following exercises, factor the greatest common factor from each polynomial. 342. 6y2+12y6In the following exercises, factor the greatest common factor from each polynomial. 343. 18x315xIn the following exercises, factor the greatest common factor from each polynomial. 344. 15m4+6m2nIn the following exercises, factor the greatest common factor from each polynomial. 345. 4x312x2+16xIn the following exercises, factor the greatest common factor from each polynomial. 346. 3x+24In the following exercises, factor the greatest common factor from each polynomial. 347. 3x3+27x212xIn the following exercises, factor the greatest common factor from each polynomial. 348. 3x(x1)+5(x1)In the following exercises, factor by grouping. 349. axay+bxbyIn the following exercises, factor by grouping. 350. x2yxy2+2x2yIn the following exercises, factor by grouping. 351. x2+7x3x21In the following exercises, factor by grouping. 352. 4x216x+3x12In the following exercises, factor by grouping. 353. m3+m2+m+1In the following exercises, factor by grouping. 354. 5x5yy+xIn the following exercises, factor each trinomial of the formx2+bx+c. 355. a2+14a+33In the following exercises, factor each trinomial of the form x2+bx+c. 356. k216k+60In the following exercises, factor each trinomial of the form x2+bx+c. 357. m2+3m54In the following exercises, factor each trinomial of the formx2+bx+c. 358. x23x10In the following examples, factor each trinomial of the form x2+bxy+cy2. 359. x2+12xy+35y2In the following examples, factor each trinomial of the formx2+bxy+cy2. 360. r2+3rs28s2In the following examples, factor each trinomial of the form x2+bxy+cy2. 361. a2+4ab21b2In the following examples, factor each trinomial of the form x2+bxy+cy2. 362. p25pq36q2In the following examples, factor each trinomial of the form x2+bxy+cy2. 363. m25mn+30n2In the following exercises, factor completely using trial and error. 364. x3+5x224xIn the following exercises, factor completely using trial and error. 365. 3y321y2+30yIn the following exercises, factor completely using trial and error. 366. 5x4+10x375x2In the following exercises, factor completely using trial and error. 367. 5y2+14y+9In the following exercises, factor completely using trial and error. 368. 8x2+25x+3In the following exercises, factor completely using trial and error. 369. 10y253y11In the following exercises, factor completely using trial and error. 370. 6p219pq+10q2In the following exercises, factor completely using trial and error. 371. 81a2+153a+18In the following exercises, factor. 372. 2x2+9x+4In the following exercises, factor. 373. 18a29a+1In the following exercises, factor. 374. 15p2+2p8In the following exercises, factor. 375. 15x2+6x2In the following exercises, factor. 376. 8a2+32a+24In the following exercises, factor. 377. 3x2+3x36In the following exercises, factor. 378. 48y2+12y36In the following exercises, factor. 379. 18a257a21In the following exercises, factor. 380. 3n412n396n2In the following exercises, factor using substitution. 381. x413x230In the following exercises, factor using substitution. 382. (x3)25(x3)36In the following exercises, factor completely using the perfect square trinomials pattern. 383. 25x2+30x+9In the following exercises, factor completely using the perfect square trinomials pattern. 384. 36a284ab+49b2In the following exercises, factor completely using the perfect square trinomials pattern. 385. 40x2+360x+810In the following exercises, factor completely using the perfect square trinomials pattern. 386. 5k370k2+245kIn the following exercises, factor completely using the perfect square trinomials pattern. 387. 75u430u3v+3u2v2In the following exercises, factor completely using the difference of squares pattern, if possible. 388. 81r225In the following exercises, factor completely using the difference of squares pattern, if possible. 389. 169m2n2In the following exercises, factor completely using the difference of squares pattern, if possible. 390. 25p21In the following exercises, factor completely using the difference of squares pattern, if possible. 391. 9121y2In the following exercises, factor completely using the difference of squares pattern, if possible. 392. 20x2125In the following exercises, factor completely using the difference of squares pattern, if possible. 393. 169n3nIn the following exercises, factor completely using the difference of squares pattern, if possible. 394. 6p2q254p2In the following exercises, factor completely using the difference of squares pattern, if possible. 395. 24p2+54In the following exercises, factor completely using the difference of squares pattern, if possible. 396. 49x281y2In the following exercises, factor completely using the difference of squares pattern, if possible. 397. 16z41In the following exercises, factor completely using the difference of squares pattern, if possible. 398. 48m4n2243n2In the following exercises, factor completely using the difference of squares pattern, if possible. 399. a2+6a+99b2In the following exercises, factor completely using the difference of squares pattern, if possible. 400. x216x+64y2In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 401. a3125In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 402. b3216In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 403. 2m3+54In the following exercises, factor completely using the sums and differences of cubes pattern, if possible. 404. 81m3+3In the following exercises, factor completely. 405. 24x3+44x2In the following exercises, factor completely. 406. 24a49a3In the following exercises, factor completely. 407. 16n256mn+49m2In the following exercises, factor completely. 408. 6a225a9In the following exercises, factor completely. 409. 5u445u2In the following exercises, factor completely. 410. n481In the following exercises, factor completely. 411. 64j2+225In the following exercises, factor completely. 412. 5x2+5x60In the following exercises, factor completely. 413. b364In the following exercises, factor completely. 414. m3+125In the following exercises, factor completely. 415. 2b22bc+5cb5c2In the following exercises, factor completely. 416. 48x5y2243xy2In the following exercises, factor completely. 417. 5q215q90In the following exercises, factor completely. 418. 4u5v+4u2v3In the following exercises, factor complete 419. 10m46250In the following exercises, factor completely. 420. 60x2y75xy+30yIn the following exercises, factor completely. 421. 16x224xy+9y264In the following exercises, solve. 422. (a3)(a+7)=0In the following exercises, solve. 423. (5b+1)(6b+1)=0In the following exercises, solve. 424. 6m(12m5)=0In the following exercises, solve. 425. (2x1)2=0In the following exercises, solve. 426. 3m(2m5)(m+6)=0In the following exercises, solve. 427. x2+9x+20=0In the following exercises, solve. 428. y2y72=0In the following exercises, solve. 429. 2p211p=40In the following exercises, solve. 430. q3+3q2+2q=0In the following exercises, solve. 431. 144m225=0In the following exercises, solve. 432. 4n2=36In the following exercises, solve. 433. (x+6)(x3)=8In the following exercises, solve. 434. (3x2)(x+4)=12xIn the following exercises, solve. 435. 16p3=24p2+9pIn the following exercises, solve. 436. 2y3+2y2=12yIn the following exercises, solve. 437. For the function, f(x)=x2+11x+20 , (a) find when f(x)=8 (b) Use this information to find two points that lie on the graph of the function.In the following exercises, solve. 438. For the function, f(x)=9x218x+5 , (a) find when f(x)=3 (b) Use this information to find two points that lie on the graph of the function.In each function, find: (a) the zeros of the function (b) the x-intercepts of the graph of the function (c) the y-intercept of the graph of the function. 439. f(x)=64x249In each function, find: (a) the zeros of the function (b) the x-intercepts of the graph of the function (c) the y-intercept of the graph of the function. 440. f(x)=6x213x5In the following exercises, solve. 441. The product of two consecutive numbers is 399. Find the numbers.In the following exercises, solve. 442. The area of a rectangular shaped patio 432 square feet. The length of the patio is 6 feet more than its width. Find the length and width.In the following exercises, solve. 443. A ladder leans against the wall of a building. The length of the ladder is 9 feet longer than the distance of the bottom of the ladder from the building. The distance of the top of the ladder reaches up the side of the building is 7 feet longer than the distance of the bottom of the ladder from the building. Find the lengths of all three sides of the triangle formed by the ladder leaning against the building.In the following exercises, solve. 444. Shruti is going to throw a ball from the top of a cliff. When she throws the ball from 80 feet above the ground, the function h(t)=16t2+64t+80 models the height, h, of the ball above the ground as a function of time, t. Find: (a) the zeros of this function which tells us when the ball will hit the ground. (b) the time(s) the ball will be 80 feet above the ground. (c) the height the ball will be at t=2 seconds which is when the ball will be at its highest point.In the following exercises, factor completely. 445. 80a2+120a3In the following exercises, factor completely. 446. 5m(m1)+3(m1)In the following exercises, factor completely. 447. x2+13x+36In the following exercises, factor completely. 448. p2+pq12q2In the following exercises, factor completely. 449. xy8y+7x56In the following exercises, factor completely. 450. 40r2+810In the following exercises, factor completely. 451. 9s212s+4In the following exercises, factor completely. 452. 6x211x10In the following exercises, factor completely. 453. 3x275y2In the following exercises, factor completely. 454. 6u2+3u18In the following exercises, factor completely. 455. x3+125In the following exercises, factor completely. 456. 32x5y2162xy2In the following exercises, factor completely. 457. 6x419x2+15In the following exercises, factor completely. 458. 3x336x2+108xIn the following exercises, solve 459. 5a2+26a=24In the following exercises, solve 460. The product of two consecutive integers is 156. Find the integers.In the following exercises, solve 461. The area of a rectangular place mat is 168 square inches. Its length is two inches longer than the width. Find the length and width of the placemat.In the following exercises, solve 462. Jing is going to throw a ball from the balcony of her condo. When she throws the ball from 80 feet above the ground, the function h(t)=16t2+64t+80 models the height, h, of the ball above the ground as a function of time, t. Find: (a) the zeros of this function which tells us when the ball will hit the ground. (b) the time(s) the ball will be 128 feet above the ground. (c) the height the ball will be at t=4 seconds.In the following exercises, solve 463. For the function, f(x)=x27x+5 , (a) find when f(x)=7 (b) Use this information to find two points that lie on the graph of the function.In the following exercises, solve 464. For the function f(x)=25x281 , find: (a) the zeros of the function (b) the x-intercepts of the graph of the function (c) the y-intercept of the graph of the function.Simplify: x2x2x23x+2 .Simplify: x23x10x2+x2 .Simplify: 2x212xy+18y23x227y2 .Simplify: 5x230xy+25y22x250y2 .Simplify: x24x525x2 .Simplify: x2+x21x2 .Simplify: 5xx2+5x+6x2410x .Simplify: 9x2x2+11x+30x2363x2 .Simplify: 2x2+5x12x216x28x+162x213x+15 .Simplify: 4b2+7b21b2b22b+14b2+15b4 .Simplify: x383x26x+12x246 .Simplify: 2z2z21z3z2+zz3+1 .Simplify: 3x2+7x+24x+243x214x5x2+x30 .Simplify: y2362y2+11y62y22y608y4 .Perform the indicated operations: 4m+43m15m23m10m24m3212m366m48 .Perform the indicated operations: 2n2+10nn1n2+10n+24n2+8n9n+48n2+12n .Find the domain of R(x)=2x210x4x216x20 .Find the domain of R(x)=4x216x8x216x64 .Find R(x)=f(x)g(x) where f(x)=3x21x29x+14 and g(x)=2x283x+6 .Find R(x)=f(x)g(x) where f(x)=x2x3x2+27x30 and g(x)=2x2100x210x .Find R(x)=f(x)g(x) where f(x)=2x2x28x and g(x)=8x2+24xx2+x6 .Find R(x)=f(x)g(x) where f(x)=15x23x2+33x and g(x)=5x5x2+9x22 .In the following exercises, determine the values for which the rational expression is undefined. 1. (a) 2x2z (b) 4p16p5 (c) n3n2+2n8In the following exercises, determine the values for which the rational expression is undefined. 2. (a) 10m11n (b) 6y+134y9 (c) b8b236In the following exercises, determine the values for which the rational expression is undefined. 3. (a) 4x2y3y (b) 3x22x+1 (c) u1u23u28In the following exercises, determine the values for which the rational expression is undefined. 4. (a) 5pq29q (b) 7a43a+5 (c) 1x24In the following exercises, simplify each rational expression. 5. 4455In the following exercises, simplify each rational expression. 6. 5663In the following exercises, simplify each rational expression. 7. 8m3n12mn2In the following exercises, simplify each rational expression. 8. 36v3w227vw3In the following exercises, simplify each rational expression. 9. 8n963n36In the following exercises, simplify each rational expression. 10. 12p2405p100In the following exercises, simplify each rational expression. 11. x2+4x5x22x+1In the following exercises, simplify each rational expression. 12. y2+3y4y26y+5In the following exercises, simplify each rational expression. 13. a24a2+6a16In the following exercises, simplify each rational expression. 14. y22y3y29In the following exercises, simplify each rational expression. 15. p3+3p2+4p+12p2+p6In the following exercises, simplify each rational expression. 16. x32x225x+50x225In the following exercises, simplify each rational expression. 17. 8b232b2b26b80In the following exercises, simplify each rational expression. 18. 5c210c10c2+30c+100In the following exercises, simplify each rational expression. 19. 3m2+30mn+75n24m2100n2In the following exercises, simplify each rational expression. 20. 5r2+30rs35s2r249s2In the following exercises, simplify each rational expression. 21. a55aIn the following exercises, simplify each rational expression. 22. 5dd5In the following exercises, simplify each rational expression. 23. 205yy216In the following exercises, simplify each rational expression. 24. 4v3264v2In the following exercises, simplify each rational expression. 25. w3+216w236In the following exercises, simplify each rational expression. 26. v3+125v225In the following exercises, simplify each rational expression. 27. z29z+2016z2In the following exercises, simplify each rational expression. 28. a25a3681a2In the following exercises, multiply the rational expressions. 29. 1216410In the following exercises, multiply the rational expressions. 30. 3251624In the following exercises, multiply the rational expressions. 31. 5x2y412xy36x220y2In the following exercises, multiply the rational expressions. 32. 12a3bb22ab29b3In the following exercises, multiply the rational expressions. 33. 5p2p25p36p21610pIn the following exercises, multiply the rational expressions. 34. 3q2q2+q6q299qIn the following exercises, multiply the rational expressions. 35. 2y210yy2+10y+25y+56yIn the following exercises, multiply the rational expressions. 36. z2+3zz23z4z4z2In the following exercises, multiply the rational expressions. 37. 284b3b3b2+8b9b249In the following exercises, multiply the rational expressions. 38. 72m12m28m+32m2+10m+24m236In the following exercises, multiply the rational expressions. 39. c210c+25c225c2+10c+253c214c5In the following exercises, multiply the rational expressions. 40. 2d2+d3d216d28d+162d29d18In the following exercises, multiply the rational expressions. 41. 2m23m22m2+7m+33m214m+153m2+17m20In the following exercises, multiply the rational expressions. 42. 2n23n1425n2n210n+252n213n+21In the following exercises, divide the rational expressions. 43. v511vv225v11In the following exercises, divide the rational expressions. 44. 10+ww8100w28wIn the following exercises, divide the rational expressions. 45. 3s2s216s34s2+16ss364In the following exercises, divide the rational expressions. 46. r2915r3275r2+15r+45In the following exercises, divide the rational expressions. 47. p3+q33p2+3pq+3q2p2q212In the following exercises, divide the rational expressions. 48. v38w32v2+4vw+8w2v24w24In the following exercises, divide the rational expressions. 49. x2+3x104x(2x2+20x+50)In the following exercises, divide the rational expressions. 50. 2y210yz48z22y1(4y232yz)In the following exercises, divide the rational expressions. 51. 2a2a215a+20a2+7a+12a2+8a+16In the following exercises, divide the rational expressions. 52. 3b2+2b812b+183b2+2b82b27b15In the following exercises, divide the rational expressions. 53. 12c2122c23c+14c+46c213c+5In the following exercises, divide the rational expressions. 54. 4d2+7d235d+10d247d212d4For the following exercises, perform the indicated operations. 55. 10m2+80m3m9m2+4m21m29m+205m2+10m2m10For the following exercises, perform the indicated operations. 56. 4n2+32n3n+23n2n2n2+n30108n224nn+6For the following exercises, perform the indicated operations. 57. 12p2+3pp+3p2+2p63p2p12p79p39p2For the following exercises, perform the indicated operations. 58. 6q+39q29qq2+14q+33q2+4q54q2+12q12q+6In the following exercises, find the domain of each function. 59. R(x)=x32x225x+50x225In the following exercises, find the domain of each function. 60. R(x)=x3+3x24x12x24In the following exercises, find the domain of each function. 61. R(x)=3x2+15x6x2+6x36In the following exercises, find the domain of each function. 62. R(x)=8x232x2x26x80