Consider the polynomial function g(x)=2x^3-9x^2+7x+6 The function g(x), has a zero of x = 2 that has a multiplicity of 1. Rewrite g(x) in completely factored form.

Answer 1

(x-2)(2x^2-5x-3) found by long or synthetic division, then factor the quadratic to get

(x-2)(2x+1)(x-3) which means x=2 is one zero, the other two zeros are 3 and -1/2

Answer 2

Using synthetic division by 2 in original equation you end up with 2x^2 - 5x -3 = 0

factoring that you get 2x^2 -6x + x - 3 = 0

2x (x - 3) + x-3 = 0

(2x + 1) (x - 3) = 0

so full factored form is (x-2)(2x+1)(x-3)