Answer to Question #171670 in Algebra for Moel Tariburu

Question

(x+2) is a factor of the cubic function f(x) = x³ + 2x²-3x +1. Use the reminder theorem to completely factorise the polynomial.

Answer 1

$\dfrac{x^3 +2x^2-3x+1}{x+2} = \dfrac{x^3 +2 x^2}{x+2} + \dfrac{1-3x}{x+2} = \dfrac{x^2(x+2)}{x+2} + \dfrac{1-3(x+2)+6}{x+2} = \dfrac{x^2(x+2)}{x+2} + \dfrac{-3(x+2)}{x+2} + \dfrac{7}{x+2}$

$\implies x^3 + 2x^2- 3x +1 = (x^2-3)(x+2) +7$