Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Elementary Algebra
Factor: 4x2+12x+9 .Factor: 9y2+24y+16 .Factor: 64y280y+25 .Factor: 16z272z+81 .Factor: 49x2+84xy+36y2 .Factor: 64m2+112mn+49n2 .Factor: 16r2+30rs+9s2 .Factor: 9u2+87u+100 .Factor: 8x2y24xy+18y .Factor: 27p2q+90pq+75q .Factor: h281 .Factor: k2121 .Factor: m21 .Factor: 81y21 .Factor: 196m225n2 .Factor: 144p29q2 .Factor: 144x2 .Factor: 169p2 .Factor: a4b4 .Factor: x416 .Factor: 7xy2175x .Factor: 45a2b80b .Factor: 8a2+20 .Factor: 36y2+81 .Factor: x3+27 .Factor: y3+8 .Factor: u3125 .Factor: v3343 .Factor: 6427x3 .Factor: 278y3 .Factor: 8x327y3 .Factor: 1000m3125n3 .Factor: 500p3+4q3 .Factor: 432c3+686d3 .In the following exercises, factor. 215. 16y2+24y+9In the following exercises, factor. 216. 25v2+20v+4In the following exercises, factor. 217. 36s2+84s+49In the following exercises, factor. 218. 49s2+154s+121In the following exercises, factor. 219. 100x220x+1In the following exercises, factor. 220. 64z216z+1In the following exercises, factor. 221. 25n2120n+144In the following exercises, factor. 222. 4p252p+169In the following exercises, factor. 223. 49x228xy+4y2In the following exercises, factor. 224. 25r260rs+36s2In the following exercises, factor. 225. 25n2+25n+4In the following exercises, factor. 226. 100y252y+1In the following exercises, factor. 227. 64m234m+1In the following exercises, factor. 228. 100x225x+1In the following exercises, factor. 229. 10k2+80k+160In the following exercises, factor. 230. 64x296x+36In the following exercises, factor. 231. 75u330u2v+3uv2In the following exercises, factor. 232. 90p3+300p2q+250pq2In the following exercises, factor. 233. x216In the following exercises, factor. 234. n29In the following exercises, factor. 235. 25v21In the following exercises, factor. 236. 169q21In the following exercises, factor. 237. 121x2144x2In the following exercises, factor. 238. 49x281y2In the following exercises, factor. 239. 169c236d2In the following exercises, factor. 240. 36p249q2In the following exercises, factor. 241. 449x2In the following exercises, factor. 242. 12125s2In the following exercises, factor. 243. 16z41In the following exercises, factor. 244. m4n4In the following exercises, factor. 245. 5q245In the following exercises, factor. 246. 98r372rIn the following exercises, factor. 247. 24p2+54In the following exercises, factor. 248. 20b2+140In the following exercises, factor. 249. x3+125In the following exercises, factor. 250. n3+512In the following exercises, factor. 251. z327In the following exercises, factor. 252. v3216In the following exercises, factor. 253. 8343t3In the following exercises, factor. 254. 12527w3In the following exercises, factor. 255. 8y3125z3In the following exercises, factor. 256. 27x364y3In the following exercises, factor. 257. 7k3+56In the following exercises, factor. 258. 6x348y3In the following exercises, factor. 259. 216y3In the following exercises, factor. 260. 2x316y3In the following exercises, factor. 261. 64a225In the following exercises, factor. 262. 121x2144In the following exercises, factor. 263. 27q23In the following exercises, factor. 264. 4p2100In the following exercises, factor. 265. 16x272x+81In the following exercises, factor. 266. 36y2+12y+1In the following exercises, factor. 267. 8p2+2In the following exercises, factor. 268. 81x2+169In the following exercises, factor. 269. 1258y3In the following exercises, factor. 270. 27u3+1000In the following exercises, factor. 271. 45n2+60n+20In the following exercises, factor. 272. 48q324q2+3qLandscaping Sue and Alan are planning to put a 15 foot square swimming pool in their backyard. They will surround the pool with a tiled deck, the same width on all sides. If the width of the deck is w, the total area of the pool and deck is given by the trinomial 4w2+60w+225 . Factor the trinomial.Home repair The height a twelve foot ladder can reach up the side of a building if the ladder’s base is b feet from the building is the square root of the binomial 144b2 . Factor the binomial.Why was it important to practice using the binomial squares pattern in the chapter on multiplying polynomials?How do you recognize the binomial squares pattern?Explain why n2+25(n+5)2 . Use algebra, words, or pictures.Maribel factored y230y+81 as (y9)2 . Was she right or wrong? How do you know?Factor completely: 3a4+18a3 .Factor completely: 45b6+27b5 .Factor completely: 10a217a+6 .Factor completely: 8x218x+9 .Factor completely: x3+36x .Factor completely: 27y2+48 .Factor completely: 16x336x .Factor completely: 27y248 .Factor completely: 4x2+20xy+25y2 .Factor completely: 9m2+42mn+49n2 .Factor completely: 8y2+16y24 .Factor completely: 5u215u270 .Factor completely: 250m3+432 .Factor completely: 81q3+192 .Factor completely: 4a464 .Factor completely: 7y47 .Factor completely: 6x212xc+6bx12bc .Factor completely: 16x2+24xy4x6y .Factor completely: 4p216p+12 .Factor completely: 6q29q6 .In the following exercises, factor completely. 279. 10x4+35x3In the following exercises, factor completely. 280. 18p6+24p3In the following exercises, factor completely. 281. y2+10y39In the following exercises, factor completely. 282. b217b+60In the following exercises, factor completely. 283. 2n2+13n7In the following exercises, factor completely. 284. 8x29x3In the following exercises, factor completely. 285. a4+9a3In the following exercises, factor completely. 286. 75m3+12mIn the following exercises, factor completely. 287. 121r2s2In the following exercises, factor completely. 288. 49b236a2In the following exercises, factor completely. 289. 8m232In the following exercises, factor completely. 290. 36q2100In the following exercises, factor completely. 291. 25w260w+36In the following exercises, factor completely. 292. 49b2112b+64In the following exercises, factor completely. 293. m2+14mn+49n2In the following exercises, factor completely. 294. 64x2+16xy+y2In the following exercises, factor completely. 295. 7b2+7b42In the following exercises, factor completely. 296. 3n2+30n+72In the following exercises, factor completely. 297. 3x381In the following exercises, factor completely. 298. 5t340In the following exercises, factor completely. 299. k416In the following exercises, factor completely. 300. m481In the following exercises, factor completely. 301. 15pq15p+12q12In the following exercises, factor completely. 302. 12ab6a+10b5In the following exercises, factor completely. 303. 4x2+40x+84In the following exercises, factor completely. 304. 5q215q90In the following exercises, factor completely. 305. u5+u2In the following exercises, factor completely. 306. 5n3+320In the following exercises, factor completely. 307. 4c2+20cd+81d2In the following exercises, factor completely. 308. 25x2+35xy+49y2In the following exercises, factor completely. 309. 10m46250In the following exercises, factor completely. 310. 3v4768Watermelon drop A springtime tradition at the University of California San Diego is the Watermelon Drop, where a watermelon is dropped from the seventh story of Urey Hall. (a) The binomial 16t2+80 gives the height of the watermelon t seconds after it is dropped. Factor the greatest common factor from this binomial. (b) If the watermelon is thrown down with initial velocity 8 feet per second, its height after t seconds is given by the trinomial 16t28t+80 . Completely factor this trinomial.Pumpkin drop A fall tradition at the University of California San Diego is the Pumpkin Drop, where a pumpkin is dropped from the eleventh story of Tioga Hall. (a) The binomial 16t2+128 gives the height of the pumpkin t seconds after it is dropped. Factor the greatest common factor from this binomial. (b) If the pumpkin is thrown down with initial velocity 32 feet per second, its height after t seconds is given by the trinomial 16t232t+128 . Completely factor this trinomial.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 it?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.Solve: (x3)(x+5)=0 .Solve: (y6)(y+9)=0 .Solve: (3m2)(2m+1)=0 .Solve: (4p+3)(4p3)=0 .Solve: 2u(5u1)=0 .Solve: w(2w+3)=0 .Solve: (x+1)2=0 .Solve: (v2)2=0 .Solve: x2x12=0 .Solve: b2+9b+14=0 .Solve: 3c2=10c8 .Solve: 2d25d=3 .Solve: 6a2+9a=3a .Solve: 45b22b=17b .Solve: 25p2=49 .Solve: 36x2=121 .Solve: (2m+1)(m+3)=12m .Solve: (k+1)(k1)=8 .Solve: 8x3=24x218x .Solve: 16y2=32y3+2y .Solve: 18a230=33a .Solve: 123b=660b2 .The product of two consecutive integers is 240. Find the integers.The product of two consecutive integers is 420. 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.A boat’s sail is a right triangle. The length of one side of the sail is 7 feet more than the other side. The hypotenuse is 13. Find the lengths of the two sides of the sail.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 one of the other legs. Find the lengths of the hypotenuse and the other leg.In the following exercises, solve. 315. (x3)(x+7)=0In the following exercises, solve. 316. (y11)(y+1)=0In the following exercises, solve. 317. (3a10)(2a7)=0In the following exercises, solve. 318. (5b+1)(6b+1)=0In the following exercises, solve. 319. 6m(12m5)=0In the following exercises, solve. 320. 2x(6x3)=0In the following exercises, solve. 321. (y3)2=0In the following exercises, solve. 322. (b+10)2=0In the following exercises, solve. 323. (2x1)2=0In the following exercises, solve. 324. (3y+5)2=0In the following exercises, solve. 325. x2+7x+12=0In the following exercises, solve. 326. y28y+15=0In the following exercises, solve. 327. 5a226a=24In the following exercises, solve. 328. 4b2+7b=3In the following exercises, solve. 329. 4m2=17m15In the following exercises, solve. 330. n2=56nn2=5n6In the following exercises, solve. 331. 7a2+14a=7aIn the following exercises, solve. 332. 12b215b=9bIn the following exercises, solve. 333. 49m2=144In the following exercises, solve. 334. 625=x2In the following exercises, solve. 335. (y3)(y+2)=4yIn the following exercises, solve. 336. (p5)(p+3)=7In the following exercises, solve. 337. (2x+1)(x3)=4xIn the following exercises, solve. 338. (x+6)(x3)=8In the following exercises, solve. 339. 16p3=24p2+9pIn the following exercises, solve. 340. m32m2=mIn the following exercises, solve. 341. 20x260x=45In the following exercises, solve. 342. 3y218y=27In the following exercises, solve. 343. The product of two consecutive integers is 56. Find the integers.In the following exercises, solve. 344. The product of two consecutive integers is 42. Find the integers.In the following exercises, solve. 345. 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. 346. 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. 347. 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. 348. 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. 349. (x+8)(x3)=0In the following exercises, solve. 350. (3y5)(y+7)=0In the following exercises, solve. 351. p2+12p+11=0In the following exercises, solve. 352. q212q13=0In the following exercises, solve. 353. m2=6m+16In the following exercises, solve. 354. 4n2+19n=5In the following exercises, solve. 355. a3a242a=0In the following exercises, solve. 356. 4b260b+224=0In the following exercises, solve. 357. The product of two consecutive integers is 110. Find the integers.In the following exercises, solve. 358. The length of one leg of a right triangle is three more than the other leg. If the hypotenuse is 15, find the lengths of the two legs.Area of a patio If each side of a square patio is increased by 4 feet, the area of the patio would be 196 square feet. Solve the equation (s+4)2=196 for s to find the length of a side of the patio.Watermelon drop A watermelon is dropped from the tenth story of a building. Solve the equation 16t2+144=0 for t to find the number of seconds it takes the watermelon to reach the ground.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. 363. 42, 60In the following exercises, find the greatest common factor. 364. 450, 420In the following exercises, find the greatest common factor. 365. 90, 150, 105In the following exercises, find the greatest common factor. 366. 60, 294, 630In the following exercises, factor the greatest common factor from each polynomial. 367. 24x42In the following exercises, factor the greatest common factor from each polynomial. 368. 35y+84In the following exercises, factor the greatest common factor from each polynomial. 369. 15m4+6m2nIn the following exercises, factor the greatest common factor from each polynomial. 370. 24pt4+16t7In the following exercises, factor by grouping. 371. axay+bxbyIn the following exercises, factor by grouping. 372. x2yxy2+2x2yIn the following exercises, factor by grouping. 373. x2+7x3x21In the following exercises, factor by grouping. 374. 4x216x+3x12In the following exercises, factor by grouping. 375. m3+m2+m+1In the following exercises, factor by grouping. 376. 5x5yy+xIn the following exercises, factor each trinomial of the form x2+bx+c. 377. u2+17u+72In the following exercises, factor each trinomial of the form x2+bx+c. 378. a2+14a+33In the following exercises, factor each trinomial of the form x2+bx+c. 379. k216k+60In the following exercises, factor each trinomial of the form x2+bx+c. 380. r211r+28In the following exercises, factor each trinomial of the form x2+bx+c. 381. y2+6y7In the following exercises, factor each trinomial of the form x2+bx+c. 382. m2+3m54In the following exercises, factor each trinomial of the form x2+bx+c. 383. s22s8In the following exercises, factor each trinomial of the form x2+bx+c. 384. x23x10In the following examples, factor each trinomial of the form x2+bxy+cy2. 385. x2+12xy+35y2In the following examples, factor each trinomial of the form x2+bxy+cy2. 386. u2+14uv+48v2In the following examples, factor each trinomial of the form x2+bxy+cy2. 387. a2+4ab21b2In the following examples, factor each trinomial of the form x2+bxy+cy2. 388. p25pq36q2In the following exercises, identify the best method to use to factor each polynomial. 389. y217y+42In the following exercises, identify the best method to use to factor each polynomial. 390. 12r2+32r+5In the following exercises, identify the best method to use to factor each polynomial. 391. 8a3+72aIn the following exercises, identify the best method to use to factor each polynomial. 392. 4mmn3n+12In the following exercises, factor completely. 393. 6x2+42x+60In the following exercises, factor completely. 394. 8a2+32a+24In the following exercises, factor completely. 395. 3n412n396n2In the following exercises, factor completely. 396. 5y4+25y270yIn the following exercises, factor. 397. 2x2+9x+4In the following exercises, factor. 398. 3y2+17y+10In the following exercises, factor. 399. 18a29a+1In the following exercises, factor. 400. 8u214u+3In the following exercises, factor. 401. 15p2+2p8In the following exercises, factor. 402. 15x2+6x2In the following exercises, factor. 403. 40s2s6In the following exercises, factor. 404. 20n27n3In the following exercises, factor. 405. 3x2+3x36In the following exercises, factor. 406. 4x2+4x8In the following exercises, factor. 407. 60y285y25In the following exercises, factor. 408. 18a257a21In the following exercises, factor. 409. 25x2+30x+9In the following exercises, factor. 410. 16y2+72y+81In the following exercises, factor. 411. 36a284ab+49b2In the following exercises, factor. 412. 64r2176rs+121s2In the following exercises, factor. 413. 40x2+360x+810In the following exercises, factor. 414. 75u2+180u+108In the following exercises, factor. 415. 2y316y2+32yIn the following exercises, factor. 416. 5k370k2+245kIn the following exercises, factor. 417. 81r225In the following exercises, factor. 418. 49a2144In the following exercises, factor. 419. 169m2n2In the following exercises, factor. 420. 64x2y2In the following exercises, factor. 421. 25p21In the following exercises, factor. 422. 116s2In the following exercises, factor. 423. 9121y2In the following exercises, factor. 424. 100k281In the following exercises, factor. 425. 20x2125In the following exercises, factor. 426. 18y298In the following exercises, factor. 427. 49u39uIn the following exercises, factor. 428. 169n3nIn the following exercises, factor. 429. a3125In the following exercises, factor. 430. b3216In the following exercises, factor. 431. 2m3+54In the following exercises, factor. 432. 81x3+3