4.12 Practice Question Solutions

Verbal Question Solutions

1. The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, $4x^2$ and $−9y^2$ don’t have a common factor, but the whole polynomial is still factorable: $4x^2−9y^2=(2x+3y)(2x−3y)$.

3. Divide the $x$ term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.

Algebraic Question Solutions

5. $7m$

7. $10m^3$

9. $y$

11. $(2a−3)(a+6)$

13. $(3n−11)(2n+1)$

15. $(p+1)(2p−7)$

17. $(5h+3)(2h−3)$

19. $(9d−1)(d−8)$

21. $(12t+13)(t−1)$

23. $(4x+10)(4x−10)$

25. $(11p+13)(11p−13)$

27. $(19d+9)(19d−9)$

29. $(12b+5c)(12b−5c)$

31. $(7n+12)^2$

33. $(15y+4)^2$

35. $(5p−12)^2$

37. $(x+6)(x^2−6x+36)$

39. $(5a+7)(25a^2−35a+49)$

41. $(4x−5)(16x^2+20x+25)$

43. $(5r+12s)(25r^2−60rs+144s^2)$

45. $(2c+3)^\frac{−1}{4}(−7c−15)$

47. $(x+2)^\frac{−2}{5}(19x+10)$

49. $(2z−9)^\frac{−3}{2}(27z−99)$

Real World Application Solutions

51. $(14x−3)(7x+9)$

53. $(3x+5)(3x−5)$

Extension Question Solutions

55. $(2x+5)^2(2x−5)^2$

57. $(4z^2+49a^2)(2z+7a)(2z−7a)$

59. $\frac{1}{(4x+9)(4x−9)(2x+3)}$