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Guías de estudio > College Algebra

Section Exercises

1. If the terms of a polynomial do not have a GCF, does that mean it is not factorable? Explain. 2. A polynomial is factorable, but it is not a perfect square trinomial or a difference of two squares. Can you factor the polynomial without finding the GCF? 3. How do you factor by grouping? For the following exercises, find the greatest common factor. 4. 14x+4xy−18xy214x+4xy - 18x{y}^{2} 5. 49mb2−35m2ba+77ma249m{b}^{2}-35{m}^{2}ba+77m{a}^{2} 6. 30x3y−45x2y2+135xy330{x}^{3}y - 45{x}^{2}{y}^{2}+135x{y}^{3}\\ 7. 200p3m3−30p2m3+40m3200{p}^{3}{m}^{3}-30{p}^{2}{m}^{3}+40{m}^{3}\\ 8. 36j4k2−18j3k3+54j2k436{j}^{4}{k}^{2}-18{j}^{3}{k}^{3}+54{j}^{2}{k}^{4} 9. 6y4−2y3+3y2−y6{y}^{4}-2{y}^{3}+3{y}^{2}-y For the following exercises, factor by grouping. 10. 6x2+5x−46{x}^{2}+5x - 4 11. 2a2+9a−182{a}^{2}+9a - 18 12. 6c2+41c+636{c}^{2}+41c+63 13. 6n2−19n−116{n}^{2}-19n - 11 14. 20w2−47w+2420{w}^{2}-47w+24 15. 2p2−5p−72{p}^{2}-5p - 7 For the following exercises, factor the polynomial. 16. 7x2+48x−77{x}^{2}+48x - 7 17. 10h2−9h−910{h}^{2}-9h - 9 18. 2b2−25b−2472{b}^{2}-25b - 247 19. 9d2−73d+89{d}^{2}-73d+8 20. 90v2−181v+9090{v}^{2}-181v+90 21. 12t2+t−1312{t}^{2}+t - 13 22. 2n2−n−152{n}^{2}-n - 15 23. 16x2−10016{x}^{2}-100 24. 25y2−19625{y}^{2}-196 25. 121p2−169121{p}^{2}-169 26. 4m2−94{m}^{2}-9 27. 361d2−81361{d}^{2}-81 28. 324x2−121324{x}^{2}-121 29. 144b2−25c2144{b}^{2}-25{c}^{2} 30. 16a2−8a+116{a}^{2}-8a+1 31. 49n2+168n+14449{n}^{2}+168n+144 32. 121x2−88x+16121{x}^{2}-88x+16 33. 225y2+120y+16225{y}^{2}+120y+16 34. m2−20m+100{m}^{2}-20m+100 35. m2−20m+100{m}^{2}-20m+100 36. 36q2+60q+2536{q}^{2}+60q+25 For the following exercises, factor the polynomials. 37. x3+216{x}^{3}+216 38. 27y3−827{y}^{3}-8 39. 125a3+343125{a}^{3}+343 40. b3−8d3{b}^{3}-8{d}^{3} 41. 64x3−12564{x}^{3}-125 42. 729q3+1331729{q}^{3}+1331 43. 125r3+1,728s3125{r}^{3}+1,728{s}^{3} 44. 4x(x−1)−23+3(x−1)134x{\left(x - 1\right)}^{-\frac{2}{3}}+3{\left(x - 1\right)}^{\frac{1}{3}} 45. 3c(2c+3)−14−5(2c+3)343c{\left(2c+3\right)}^{-\frac{1}{4}}-5{\left(2c+3\right)}^{\frac{3}{4}} 46. 3t(10t+3)13+7(10t+3)433t{\left(10t+3\right)}^{\frac{1}{3}}+7{\left(10t+3\right)}^{\frac{4}{3}} 47. 14x(x+2)−25+5(x+2)3514x{\left(x+2\right)}^{-\frac{2}{5}}+5{\left(x+2\right)}^{\frac{3}{5}} 48. 9y(3y−13)15−2(3y−13)659y{\left(3y - 13\right)}^{\frac{1}{5}}-2{\left(3y - 13\right)}^{\frac{6}{5}} 49. 5z(2z−9)−32+11(2z−9)−125z{\left(2z - 9\right)}^{-\frac{3}{2}}+11{\left(2z - 9\right)}^{-\frac{1}{2}} 50. 6d(2d+3)−16+5(2d+3)566d{\left(2d+3\right)}^{-\frac{1}{6}}+5{\left(2d+3\right)}^{\frac{5}{6}} For the following exercises, consider this scenario: Charlotte has appointed a chairperson to lead a city beautification project. The first act is to install statues and fountains in one of the city’s parks. The park is a rectangle with an area of 98x2+105x−2798{x}^{2}+105x - 27 m2, as shown in the figure below. The length and width of the park are perfect factors of the area. A rectangle that’s textured to look like a field. The field is labeled: l times w = ninety-eight times x squared plus one hundred five times x minus twenty-seven. 51. Factor by grouping to find the length and width of the park. 52. A statue is to be placed in the center of the park. The area of the base of the statue is 4x2+12x+9m24{x}^{2}+12x+9{\text{m}}^{2}. Factor the area to find the lengths of the sides of the statue. 53. At the northwest corner of the park, the city is going to install a fountain. The area of the base of the fountain is 9x2−25m29{x}^{2}-25{\text{m}}^{2}. Factor the area to find the lengths of the sides of the fountain. For the following exercise, consider the following scenario: A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yd. as shown in the figure below. The flagpole will take up a square plot with area x2−6x+9{x}^{2}-6x+9 yd2. A square that’s textured to look like a field with a missing piece in the shape of a square in the center. The sides of the larger square are labeled: 100 yards. The center square is labeled: Area: x squared minus six times x plus nine. 54. Find the length of the base of the flagpole by factoring. For the following exercises, factor the polynomials completely. 55. 16x4−200x2+62516{x}^{4}-200{x}^{2}+625 56. 81y4−25681{y}^{4}-256 57. 16z4−2,401a416{z}^{4}-2,401{a}^{4} 58. 5x(3x+2)−24+(12x+8)325x{\left(3x+2\right)}^{-\frac{2}{4}}+{\left(12x+8\right)}^{\frac{3}{2}} 59. (32x3+48x2−162x−243)−1{\left(32{x}^{3}+48{x}^{2}-162x - 243\right)}^{-1}

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