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All Textbook Solutions for High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
Find the GCF of the terms of each polynomial: 9m3+30m24Find the GCF of the terms of each polynomial. 4p3+12p218pFind the GCF of the terms of each polynomial. 252e2+12e22Find the GCF of the terms of each polynomial: 14b3+21b242bFind the GCF of the terms of each polynomial: 2712x3+24x216xFind the GCF of the terms of each polynomial: 8a4+24a340a2Find the GCF of the terms of each polynomial: 29.36j33j215jFind the GCF of the terms of each polynomial: 30.12j8+30j46j3Factor each polynomial. 12x9Factor each polynomial. 18s2+54Factor each polynomial. 33.108t260tFactor each polynomial. 34.20w2+16wFactor each polynomial. 35.32y3+8y2Factor each polynomial. 36.300d2175dFactor each polynomial. 37.12n336n2+18Factor each polynomial. 38.40t3+25t2+80tFactor each polynomial. 42x456x3+28x2Factor each polynomial. 15c4+24c36c2+12cFactor each polynomial. 41.8m3+14m2+6mFactor each polynomial. 10x2+50x25Factor each polynomial. 36p4+14p3+35p2Factor each polynomial. 44.9a5+27a4+63a2Factor each polynomial. 45.4b4+20b3+12bFactor each polynomial. 46x6x4+x2Factor each polynomial. 34g3+51g2+17gFactor each polynomial. 48.18h427h2+18hA circular hedge surrounds a sculpture on a square base. The radius of the hedge is 6x. The side length of the square sculpture base is 4x. What is the area of the hedge? Write your answer in factored form.Suppose you are making a giant chocolate chip cookie for a raffle. You roll out a square slab of cookie dough. Then you use a circular plate that touches the edges of the square slab of cookie dough and cut the cookie out of the dough. What is the area of the extra dough? Write your answer in factored form.Simplify. Write in standard form. 3x4x26x+12Simplify. Write in standard form. 52.7y24y3+6ySimplify. Write in standard form. 9a3a2+a5Simplify. Write in standard form. p(p+4)2p(p8)Simplify. Write in standard form. 55.t(t+4)t4t22Simplify. Write in standard form. 566c2c24c(8c)Simplify. Write in standard form. 5m2m37m2+mSimplify. Write in standard form. 2q(q+1)q(q1)Simplify. Write in standard form. n26n2+2nFactor each polynomial. 60.15xy4+60x2y3Factor each polynomial. 8m3n4+32mn2Factor each polynomial. 62.26a5b2+51a4Factor each polynomial. 36j2k4+24j4k2Factor each polynomial. 12w4x342wx2Factor each polynomial. 65.54c2d336c3d2Factor each polynomial. 12st4+46s3t4Factor each polynomial. 9v6u3+33v4w5Factor each polynomial. 11e3f3+132e2f4Error Analysis A student factored the polynomial at the right. Describe and correct the error made in factoring.Reasoning The GCF of two numbers j and k is 8. What is the GCF of 2 j and 2 k? Justify your answer.A cylinder has a radius of 3m2n and a height of 7 mn. The formula for the volume of a cylinder is V=r2h, where r is the radius and h is the height. What is the volume of the cylinder? Simplify your answer.For Exercises 15, choose the correct Letter. How can this product be simplified? 5x2(2x3) A. 5x2+2x3 B. 10x315x2 C. 5x2 D. 7x315x2For Exercises 1-5,choose the correct letter. What is the GCF of the terms of 8c3+12c2+10c? F. 2 G. 4 H. 2c I. 4cFor Exercises 15, choose the correct letter. How can the polynomial 6d4+9d312d2 be factored? A. 3d22d2+3d4 B. 3d23d2+6d9 C. 3dd3+3d24 D. 6d2d2+3d36For Exercises 15, choose the correct letter. There is a circular garden in the middle of a square yard. The radius of the circle is 4x .The side length of the yard is 20x .What is the area of the part of the yard that is not covered by the circle? F. 4x(5) G. 8x2(5) H. 16x(25+) I. 16x2(25)For Exercises 15, choose the correct letter. What is the simplified form of 3z2(z+2)4z2+1? A. 7z2+1 B. 3z34z26z4 C. 3z32z24 D. 3z310z24A rectangular blacktop with a length of 5x and a width of 3x has been erected inside a rectangular field that has a length of 12x and a width of 7x What is the area of the part of the field that is not blacktop? b. There is a circular fountain in the rectangular field that has a radius of 3x. What is the area of the part of the field that does not include the blacktop or the fountain? Factor your answer.Simplify each product using the Distributive Property. (x+3)(x+8)Simplify each product using the Distributive Property. (y4)(y+7)Simplify each product using the Distributive Property. (m+9)(m3)Simplify each product using the Distributive Property. (c6)(c4)Simplify each product using the Distributive Property. (2r5)(r+3)Simplify each product using the Distributive Property. (3x+1)(5x3)Simplify each product using the Distributive Property. (d+2)(4d3)Simplify each product using the Distributive Property. (5t1)(3t2)Simplify each product using the Distributive Property. (a+11)(11a+1)Simplify each product using a table. (x+3)(x5)Simplify each product using a table. (a2)(a13)Simplify each product using a table. (w4)(w+8)Simplify each product using a table. (5h3)(h+7)Simplify each product using a table. (x3)(2x+3)Simplify each product using a table. (2p+1)(6p+4)Simplify each product using the FOIL method. (2x6)(x+3)Simplify each product using the FOIL method. (n5)(3n4)Simplify each product using the FOIL method. 4p2+2(3p1)Simplify each product using the FOIL method. (a+7)(a3)Simplify each product using the FOIL method. (x+3)(3x2)Simplify each product using the FOIL method. (k9)(k+5)Simplify each product using the FOIL method. (b5)(b11)Simplify each product using the FOIL method. (4m1)(m+4)Simplify each product using the FOIL method. (7z+3)(4z6)Simplify each product using the FOIL method. (2h+6)(5h3)Simplify each product using the FOIL method. (3w+12)(w+3)Simplify each product using the FOIL method. (6c2)(9c8)What is the surface area of the cylinder at the right? Write your answer in simplified form.The radius of cylindrical popcorn tin is (3x+1) in. The height of the tin is three times the radius. What is the surface area of the cylinder? Write your answer in simplified form.The radius of a cylindrical tennis ball can is (2x+1)cm. The height of the tennis ball can is six times the radius. What is the surface area of the cylinder? Write your answer in simplified form.Simplify each product. (x+3)x22x+4Simplify each product. k25k+2)(k5)Simplify each product. 3a2+a+4(2a6)Simplify each product. 2x2+2x6(3x4)Simplify each product. 35.(4g+5)2g27g+3Simplify each product. m22m+7(3m+6)Simplify each product. (2c+8)2c24c1Simplify each product. (t+8)3t2+4t+5A medical centers rectangular parking lot currently has a length of 30 meters and a width of 20 meters. The center plans to expand both the length and the width of the parking lot by 2x meters. What polynomial in standard form represents the area of the expanded parking lot?Error Analysis Describe and correct the error made in finding the product.Multi Step The height of a painting is twice its width x. You want a 3 inch wide wooden frame for the painting. The area of the frame alone is 216 square inches. a. Draw a diagram that represents this situation. b. Write a variable expression for the area of the frame alone. c. What are the dimensions of the frame?For Exercises 15, choose the correct letter. What is the simplified form of (x2)(2x+3)? Use the Distributive Property. A. 2x2x6 B. 2x26 C. 2x27x6 D. 2x2+x6For Exercises 15, choose the correct letter. What is the simplified form of (3x+2)(4x3)? Use a table. F. 12x2+18x+6 G. 12x2+x6 H. 12x2+18x6 I. 12x2x6For Exercises 15, choose the correct letter. What is the simplified form of (4p2)(p4)? A. 4p2+6p16 B. 4p218p+8 C. 4p214p6 D. 4p26p+16For Exercises 15, choose the correct letter. The radius of a cylinder is 3x2cm. The height of the cylinder is x+3cm. What is the surface area of the cylinder? F. 23x2+10x8 G. 212x2+7x2 H. 212x22x+13 I. 212x25x2For Exercises 15, choose the correct letter. What is the simplified form of 2x2+4x3(3x+1)? A. 6x3+10x25x+3 B. 6x3+14x2+5x3 C. 6x3+14x25x3 D. 6x310x25x3A soup can that is a cylinder has a radius of 2x1 and a height of 3x. What is the surface area of the soup can? Show your work.Simplify each expression. (x+7)2Simplify each expression. (w+9)2Simplify each expression. (h+3)2Simplify each expression. (2s+4)2Simplify each expression. (3s+1)2Simplify each expression. 6.(5s+2)2Simplify each expression. (a5)2Simplify each expression. (k10)2Simplify each expression. (n4)2Simplify each expression. (3m4)2Simplify each expression. (6m2)2Simplify each expression. (4m2)2The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.A square brown tarp has a square green patch green in the corner. The side length of the tarp is (x+8) and the side length of the patch is x. What is the area of the brown part of the tarp?A square red placemat has a gold square in the centre. The side length of the gold square is (x2) inches and the width of the red region is 4 inches. What is the area of the red part of the placemat?Mental Math Simplify each product. 482Mental Math Simplify each product. 312Mental Math Simplify each product. 21.292Mental Math Simplify each product. 522Mental Math Simplify each product. 632Mental Math Simplify each product. 24.412Mental Math Simplify each product. 25.892Mental Math Simplify each product. 26.1992Mental Math Simplify each product. 27.3022Simplify each product. 28.(v+7)(v7)Simplify each product. (b+2)(b2)Simplify each product. (z9)(z+9)Simplify each product. (x+12)(x12)Simplify each product. (8+y)(8y)Simplify each product. (t15)(t+15)Simplify each product. (m+1)(m1)Simplify each product. (a+4)(a4)Simplify each product. 36.(5+g)(5g)Simplify each product. (p+20)(p20)Simplify each product. (f18)(f+18)Simplify each product. (2c+3)(2c3)Mental Math Simplify each product. 6159Mental Math Simplify each product. 2733Mental Math Simplify each product. 202198Mental Math Simplify each product. 7466Mental Math Simplify each product. 597603Mental Math Simplify each product. 85 ăƒ» 75Simplify each product. (m+4n)2Simplify each product. (3a?b)2Simplify each product. (6st)2Simplify each product. s+7t22Simplify each product. p58q32Simplify each product. e4+f22Simplify each product. r2+5sr25sSimplify each product. 6p2+2q6p22qSimplify each product. 3w4z33w4+z3Error Analysis Describe and correct the error made in simplifying the product.The formula V=43r3 gives the volume of a sphere with radius r.Find the volume of a sphere with radius x+9. Write your answer in standard form.Solve each exercise and enter your answer on the grid provided. What is coefficient of the x-term in the simplified form of (2x+4)2?Solve each exercise and enter your answer on the grid provided. What is 272? Use mental math.Solve each exercise and enter your answer on the grid provided. What is constant in the simplified form of (x6)2?Solve each exercise and enter your answer on the grid provided. What is the product of 38 and 42 Use mental math.Solve each exercise and enter your answer on the grid provided. How much greater is the product of 73 and 67 than the product of 74 and 66?Complete. 1.k2+11k+30=(k+5)(k+)Complete. 2x2+6x+9=(x+3)(x+)Complete. t2+7t+10=(t+2)(t+)Complete. n2+9n+14=(n+7)(n+)Complete. w2+13w+36=(w+4)(w+)Complete. y2+18y+65=(y+13)(y+)Complete. s212s+32=(s8)(s)Complete. g214g+45=(g9)(g)Complete. v217v+60=(v12)(v)Complete. q213q+42=(q6)(q)Complete. 11.d29d+8=(d8)(d)Complete. r29r+20=(r5)(r)Factor each expression. Check your answer. y2+5y+6Factor each expression. Check your answer. t2+9t+18Factor each expression. Check your answer. x2+16x+63Factor each expression. Check your answer. n212n+35Factor each expression. Check your answer. r212r+27Factor each expression. Check your answer. q212q+20Factor each expression. Check your answer. w2+19w+60Factor each expression. Check your answer. b211b+24Factor each expression. Check your answer. 21.z213z+12Complete. q2+q56=(q7)(q+)Complete. z23z18=(z6)(z+)Complete. n26n40=(n+4)(n)Complete. 25.y2+3y4=(y+4)(y)Complete. v25v36=(v9)(v+)Complete. d2+2d15=(d3)(d+)Complete. 28.m25m14=(m+2)(m)Complete. p26p16=(p8)(p+)Factor each expression. Check your answer. r2+3r10Factor each expression. Check your answer. w2+2w8Factor each expression. Check your answer. 32.z2+3z40Factor each expression. Check your answer. d24d12Factor each expression. Check your answer. p27p8Factor each expression. Check your answer. 35.s25s24Factor each expression. Check your answer. x2+5x6Factor each expression. Check your answer. 37.v2+3v28Factor each expression. Check your answer. n2+2n63Factor each expression. Check your answer. t22t24Factor each expression. Check your answer. 40.a27a18Factor each expression. Check your answer. 41.c2c30The area of a rectangular door is given by the trinomial x214x+45. The doors width is (x9). What is the doors length?The area of a rectangular painting is given by the trinomial a26a16. The paintings length is (a+2). What is the paintings width?Write the correct factored form for each expression. 44.k2+4kn96n2Write the correct factored form for each expression. g213gh+42h2Write the correct factored form for each expression. 46.m24mn32n2Write the correct factored form for each expression. 47x2+5xy14y2Write the correct factored form for each expression. s2+17st+72t2Write the correct factored form for each expression. h2+3hj88j2Error Analysis Describe and correct the error made in factoring the trinomial.A rectangular pool cover has an area of p2+9p36. What are possible dimensions of the pool cover? Use factoring.For Exercises 17, choose the correct letter. Which number makes this equation true? v2+10v+16=(v+8)(v+) A. 2 B. 4 C. 6 D. 8For Exercises 17, choose the correct letter. What is the factored form of x2+6x+8? F. (x+5)(x+3) G. (x+4)(x+2) H. (x+7)(x+1) ।. (x+3)(x+3)For Exercises 17, choose the correct letter. What is the factored form of x27x+12? A. (x5)(x3) B. (x6)(x1) C. (x2)(x5) D. (x4)(x3)For Exercises 17, choose the correct letter. Which number makes this equation true? q2+3q18=(q+6)(q F. 1 G. 2 H. 3 I. 12For Exercises 17, choose the correct letter. What is the factored form of x2+3x10? A. (x+5)(x2) C. (x2)(x5) B. (x5)(x+2) D. (x+5)(x+2)For Exercises 17, choose the correct letter. The area of a garden is given by the trinomial g22g24. The gardens length is g+4. What is the gardens width? F. g2 G. g6 H. g8 I. g+2For Exercises 17, choose the correct letter. What is the factored form of x2+3xy28y2? A. (x+14y)(x2y) B. (x+2y)(x14y) C. (x+4y)(x7y) D. (x4y)(x+7y)The area of a rectangular backyard is given by the trinomial b2+5b24. What are possible dimensions of the backyard? Show why your answer is correct.Factor each expression. 1.2w2+13w+15Factor each expression. 1.2w2+13w+15Factor each expression. 4n2+62n32Factor each expression. 3p27p40Factor each expression. 5r210r24Factor each expression. 6.5z217z+14Factor each expression. 14k267k+63Factor each expression. 2m2m15Factor each expression. 3x2+9x84Factor each expression. 4y2+26y+30Factor each expression. 11.5t224t5Factor each expression. 7c22c9Factor each expression. 8k242k+27Factor each expression. 6g22g20Factor each expression. 2c223c+11The area of a rectangular computer screen is 4x2+20x+16. The width of the screen is 2x+8. What is the length of the screen?The area of a rectangular granite countertop is 12x2+10x12. The width of the countertop is 2x+3. What is the length of the countertop?The area of a rectangular book cover is 4x26x40. The width of the book cover is 2x8. What is the length of the book cover?The area of a rectangular parking lot is 21x244x+15. The width of the parking lot is 3x5. What is the length of the parking lot?Factor each expression completely. 6x210x4Factor each expression completely. 6d2+21d+15Factor each expression completely: 8n2+68n+84Factor each expression completely. 20p2115p30Factor each expression completely: 24.15r2+141r90Factor each expression completely: 25.12z214z+4Factor each expression completely: 26.20k2+110k+120Factor each expression completely: 9m266m+21Factor each expression completely. 40x2136x96Factor each expression completely. 42y2+28y14Factor each expression completely. 8t216t90Factor each expression completely: 31.24c2+96c+90Open-Ended Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials. 4x2+x+12Open-Ended Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials. 33.6t2t4Open-Ended Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials. 9m2m+8Open-Ended Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials. 35.8n2+n10Open-Ended Find two diff erent values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials. 36.12v2v+15Open-Ended Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials. 5w2w24Error Analysis Describe and correct the error made in factoring the expression at the right.A parallelogram has an area of 4x2+7x15. The base of the parallelogram is x+3. What is the height of the parallelogram? a. Write the formula for the area of a parallelogram. b. Writing Explain how factoring the trinomial helps you solve the problem.A rectangular window pane has an area of 15x219x+6. The width of the window pane is 3x2. What is the length of the window pane?Factor each expression completely. 41.28y2+43y48Factor each expression completely. 16z254z+35Factor each expression completely. 27n254n+15Factor each expression completely. 36p2+63p+20Factor each expression completely. 45.28r220r33Factor each expression completely. 30z253z+12Factor each expression completely. 47.32x3+28x2+5xFactor each expression completely. 48.25p2+20pq12q2For Exercises 15, choose the correct letter. What is the factored form of 4x2+12x+5? A. (2x+4)(2x+3) B. (4x+5)(x+1) C. (2x+1)(2x+5) D. (4x+1)(x+5)For Exercises 15, choose the correct letter. What is the factored form of 4x2+12x+5? A. (2x+4)(2x+3) B. (4x+5)(x+1) C. (2x+1)(2x+5) D. (4x+1)(x+5)For Exercises 15, choose the correct letter. What is the factored form of 2x2+x3? G. (2x+1)(x3) H. (2x3)(x+1) F. (2x+3)(x1) I. (2x1)(x+3)For Exercises 15, choose the correct letter. The area of a rectangular swimming pool is 10x219x15. The length of the pool is 5x+3. What is the width of the pool? A. 2x18 B. 2x5 C. 5x5 D. 5x22For Exercises 15, choose the correct letter. What is the factored form of 16x216x12? F. 4(2x2)(2x+2) G. 4(4x6)(x+2) H. 4(2x2)(2x+3) I. 4(2x3)(2x+1)For Exercises 15, choose the correct letter. What is the factored form of 3x2+21x24? A. 3(x+8)(x1) B. 3(x+6)(x+1) C. 3(x+5)(x3) D. 3(x+7)(x3)The perimeter around a dogs running space is 20x2+28x+8. The length of the dogs running space is 10x+4. What is the width of the dogs running space? Show why your answer is correct.Factor each expression. h2+10h+25Factor each expression. v214v+49Factor each expression. d222d+121Factor each expression. m2+4m+4Factor each expression. 5q2+6q+9Factor each expression. p224p+144Factor each expression. 36x2+60x+25Factor each expression. 64x2+48x+9Factor each expression. 49n2+14n+1Factor each expression. 10.16s272s+81Factor each expression. 11.25r280r+64Factor each expression. 9g224g+16Factor each expression. 81w2+144w+64Factor each expression. 16e288e+121Factor each expression. 25j2+100j+100Factor each expression. 144f224f+1Factor each expression. 4a236a+81Factor each expression. 49d284d+36The given expression represents the area. Find the side length of the square. 64x2+80x+25The given expression represents the area. Find the side length of the square. 9y224y+16The given expression represents the area. Find the side length of the square. 4t2+36t+81The given expression represents the area. Find the side length of the square.The given expression represents the area. Find the side length of the square.