Question

Factor x^3 + 5x^2 - 2x - 24 completely, given that (x - 2) is a factor. Find all zeros,

Answer 1

The zeros of the polynomial will be 2, -4 and -3

Zeros of a polynomial

Given the polynomial function expressed as $x^3 + 5x^2 - 2x - 24$. IF x - 2 is a factor, this shows that 2 is a zero of the polynomial.

Find the quotient of $x^3 + 5x^2 - 2x - 24$ and $x-2$ as shown:
$\frac{x^3+5x^2-2x-24}{x-2} =x^2+7x+!2$

Factorize the quotient as shown:

$x^2+7x+12\\ =x^2+3x+4x+12\\ =x(x+3)+4(x+3)\\ =(x+4)(x+3)$

The zeros of the polynomial will be 2, -4 and -3

Learn more on zeros of the polynomial here: https://brainly.com/question/2833285