Mathematics

Since $x-2$ is a factor, you know that $g(2)=0$, which means you can divide $g(x)$ by $(x-2)$ using polynomial long division or synthetic division to find the quotient. That quotient will be a quadratic, which you can then factor by finding its roots or recognizing a pattern. The key is to reduce the cubic to a simpler problem you already know how to solve.

Since $x-2$ is a factor, you know that $g(2)=0$, which means you can divide $g(x)$ by $(x-2)$ using polynomial long division or synthetic division to find the quotient. That quotient will be a quadratic, which you can then factor by finding its roots or recognizing a pattern. The key is to reduce the cubic to a simpler problem you already know how to solve.