Use synthetic division to show that g(x) is a factor of f(x), and complete the factorization of f(x). g(x) = x − 6, f(x) = x3 − 4x2 − 75x + 378

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 − 6, f(x) = x³ − 4x² − 75x + 378

f(x)=

Answer 1

(6)^3 - 4(6)^2 - 75(6) + 378 = 216 - 144 - 450 + 378 = 0 so x-6 is a factor

divide into the cubic to get

x^2 + 2x -63

which factors further into (x+9)(x-7)

the cubic has 3 factors

(x-6)(x-7)(x+9)