Question

Factor 2x^3+3x^2-23x-12, given that x+4 is a factor

Answer 1

Hello,
$2x^3+3x^2-23x-12\\ =2x^3+8x^2-5x^2-20x-3x-12\\ =2x^2(x+4)-5x(x+4)-3(x+4)\\ =(x+4)(2x^2-5x-3)\\ =(x+4)(2x^2-6x+x-3)\\ =(x+4)[2x(x-3)+1(x+3)]\\ =(x+4)(x-3)(2x+1)$

Answer 2

(2x + 1) • (x - 3) • (x + 4)