Question

Find a factor of the polynomial $q\left(x\right)$, if $4$ and $0$ are both solutions to the equation $q\left(x\right)=0$

• A. $x^2$
• B. $(x-4{)}^2$
• C. $x^2+4x$
• D. $x^2-8x$
• E. $x^2-4x$

Answer 1

The correct option is E $x^2-4x$

Since $4$ is solution of $q\left(x\right)$, $(x-4)$ is a factor of $q\left(x\right)$
and $0$ is also solution of $q\left(x\right)$, $(x-0)$ is a factor of $q\left(x\right)$.
So, $x(x-4)=x^2-4x$ is a factor of $q\left(x\right)$.