Question

(x ³-x ²-24x-36)/x-6

Use synthetic division, and the given factor to completely factor the polynomial. (please help I am really struggling with this)

Answer 1

The completely factored form of the polynomial is (x - 6)(x² + 5x + 6).

Step-by-step explanation:

To completely factor the polynomial (x³ - x² - 24x - 36)/(x - 6) using synthetic division, we first need to determine the zero of the polynomial, which is the factor of the form (x - a) where a is a number that makes the polynomial equal to zero.

Using synthetic division, we divide (x³ - x² - 24x - 36) by (x - 6) and find that the remainder is zero.

This means that (x - 6) is a factor of (x³ - x² - 24x - 36).

So, the completely factored form of the polynomial is (x - 6)(x² + 5x + 6).