Factor and then check by multiplying. Show your work.
B. x^2+9x+14
C. x^27x30
D. x^212x+36
E. x^2144
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.

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

x^2  7x  30 = x^2  10x + 3x  30 = x(x10) + 3(x10) = (x10)(x+3)

x^2  12x + 36 = x^2  2.x.6 + 6^2 = (x6)^2

x^2  144 = x^2  12x + 12x  144 = x(x12) + 12(x12) = (x12)(x+12)

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

12x^2 + 108 = 12(x^2  9) = 12(x^2  3x + 3x  9) = 12(x(x3) + 3(x3)) = 12(x3)(x+3)