Factors of Polynomials uses the factor and remainder theorems.
Factor theorem: if $f(a)=0$, then $(x-a)$ is a factor. Remainder theorem: the remainder when $f(x)$ is divided by $(x-a)$ is $f(a)$. For $f(x)=x^2+2$, dividing by $(x-1)$ gives remainder $f(1)=3$.
Remember
- $f(a)=0$ ⟺ $(x-a)$ is a factor.
- Remainder $= f(a)$.