Use synthetic division to show that g(x) is a factor of f(x), and complete the factorization of f(x). g(x) = x + 2, f(x) = x3 − 3x2 − 24x − 28

Question

Use synthetic division to show that g(x) is a factor of f(x), and complete the factorization of f(x).

g(x) = x + 2, f(x) = x³ − 3x² − 24x − 28

f(x)=

Please help I got this answer x^2 - 5x - 15 and put it in and the h.w system said it was wrong. I don't know what I'm doing wrong ;(.

Answer 1

(-2)^3 -3(-2)^2 -24(-2) - 28 = -8 -12 + 48 -28 = 0, x+2 is a factor

divide and get another factor x^2 -5x -14. you can factor that further

(x-7)(x+2)

so the cubic polynomial factors into

(x-7)(x+2)(x+2) or

(x-7)(x+2)^2