Factor and then check by multiplying. Show your work

multiplying

#1

Factor and then check by multiplying. Show your work.

B. x^2+9x+14
C. x^2-7x-30
D. x^2-12x+36
E. x^2-144
F. 5x^2+40x+75
G. -12x^2+108

Answer:

I’ll leave you to show that the following factors when multiplied give the same answer.

  1. x^2 + 9x + 14 = x^2 + (7x+2x)+14 =(x+7)(x+2)

  2. x^2 - 7x - 30 = x^2 - 10x + 3x - 30 = x(x-10) + 3(x-10) = (x-10)(x+3)

  3. x^2 - 12x + 36 = x^2 - 2.x.6 + 6^2 = (x-6)^2

  4. x^2 - 144 = x^2 - 12x + 12x - 144 = x(x-12) + 12(x-12) = (x-12)(x+12)

  5. 5x^2 + 40x + 75 = 5(x^2 + 8x + 15) = 5(x^2 + 3x + 5x + 15) = 5(x+3)(x+5)

  6. -12x^2 + 108 = -12(x^2 - 9) = -12(x^2 - 3x + 3x - 9) = -12(x(x-3) + 3(x-3)) = -12(x-3)(x+3)