Question

consider the polynomial g(x)=2x^3+2x^2-28x-48(A)Use synthetic division to rewrite g as a product of a linear factor and a new smaller (quadratic) factor DO NOT finish factoring g completely here but see part( B)(B) Finish factoring G completely by factoring the quadratic from part (A)

Answer 1

$g(x)=2x^3+2x^2-28x-48$

A. we can divide between for example (x+2)

In the image, we can see the synthetic division

the result is

$g(x)=(x+2)(2x^2-2x-24)$

B. For finishing factoring g(x) we need to solve the quadratic form found in the synthetic division

so, g(x) factorize is

$g(x)=2(x+2)(x-4)(x+3)$