Factor x^3+x^2-12

Question

Hi, what are the steps to factoring something like x³ +x² -12 ? I know how to factor functions like x² + 2x + 1 but not when it has a cube root.

Answer 1

This does not have a cube root. It has a CUBIC (degree 3) term.

 

In Algebra II we learn about rational roots theorem, synthetic division, and Descartes' rule of signs.

It happens that 2 is a root, so x-2 is a factor.

When we divide this synthetically, we obtain the depressed polynomial (other) factor as x²⁺3x +6.