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. [latex]14x+4xy - 18x{y}^{2}[/latex] 5. [latex]49m{b}^{2}-35{m}^{2}ba+77m{a}^{2}[/latex] 6. [latex]30{x}^{3}y - 45{x}^{2}{y}^{2}+135x{y}^{3}\\[/latex] 7. [latex]200{p}^{3}{m}^{3}-30{p}^{2}{m}^{3}+40{m}^{3}\\[/latex] 8. [latex]36{j}^{4}{k}^{2}-18{j}^{3}{k}^{3}+54{j}^{2}{k}^{4}[/latex] 9. [latex]6{y}^{4}-2{y}^{3}+3{y}^{2}-y[/latex] For the following exercises, factor by grouping. 10. [latex]6{x}^{2}+5x - 4[/latex] 11. [latex]2{a}^{2}+9a - 18[/latex] 12. [latex]6{c}^{2}+41c+63[/latex] 13. [latex]6{n}^{2}-19n - 11[/latex] 14. [latex]20{w}^{2}-47w+24[/latex] 15. [latex]2{p}^{2}-5p - 7[/latex] For the following exercises, factor the polynomial. 16. [latex]7{x}^{2}+48x - 7[/latex] 17. [latex]10{h}^{2}-9h - 9[/latex] 18. [latex]2{b}^{2}-25b - 247[/latex] 19. [latex]9{d}^{2}-73d+8[/latex] 20. [latex]90{v}^{2}-181v+90[/latex] 21. [latex]12{t}^{2}+t - 13[/latex] 22. [latex]2{n}^{2}-n - 15[/latex] 23. [latex]16{x}^{2}-100[/latex] 24. [latex]25{y}^{2}-196[/latex] 25. [latex]121{p}^{2}-169[/latex] 26. [latex]4{m}^{2}-9[/latex] 27. [latex]361{d}^{2}-81[/latex] 28. [latex]324{x}^{2}-121[/latex] 29. [latex]144{b}^{2}-25{c}^{2}[/latex] 30. [latex]16{a}^{2}-8a+1[/latex] 31. [latex]49{n}^{2}+168n+144[/latex] 32. [latex]121{x}^{2}-88x+16[/latex] 33. [latex]225{y}^{2}+120y+16[/latex] 34. [latex]{m}^{2}-20m+100[/latex] 35. [latex]{m}^{2}-20m+100[/latex] 36. [latex]36{q}^{2}+60q+25[/latex] For the following exercises, factor the polynomials. 37. [latex]{x}^{3}+216[/latex] 38. [latex]27{y}^{3}-8[/latex] 39. [latex]125{a}^{3}+343[/latex] 40. [latex]{b}^{3}-8{d}^{3}[/latex] 41. [latex]64{x}^{3}-125[/latex] 42. [latex]729{q}^{3}+1331[/latex] 43. [latex]125{r}^{3}+1,728{s}^{3}[/latex] 44. [latex]4x{\left(x - 1\right)}^{-\frac{2}{3}}+3{\left(x - 1\right)}^{\frac{1}{3}}[/latex] 45. [latex]3c{\left(2c+3\right)}^{-\frac{1}{4}}-5{\left(2c+3\right)}^{\frac{3}{4}}[/latex] 46. [latex]3t{\left(10t+3\right)}^{\frac{1}{3}}+7{\left(10t+3\right)}^{\frac{4}{3}}[/latex] 47. [latex]14x{\left(x+2\right)}^{-\frac{2}{5}}+5{\left(x+2\right)}^{\frac{3}{5}}[/latex] 48. [latex]9y{\left(3y - 13\right)}^{\frac{1}{5}}-2{\left(3y - 13\right)}^{\frac{6}{5}}[/latex] 49. [latex]5z{\left(2z - 9\right)}^{-\frac{3}{2}}+11{\left(2z - 9\right)}^{-\frac{1}{2}}[/latex] 50. [latex]6d{\left(2d+3\right)}^{-\frac{1}{6}}+5{\left(2d+3\right)}^{\frac{5}{6}}[/latex] 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 [latex]98{x}^{2}+105x - 27[/latex] m2, as shown in the figure below. The length and width of the park are perfect factors of the area.
