Question

HELP ASAP PLEASE!!!

Use the Remainder Theorem to determine if (x + 6) is a factor of x3 + 7x2+ 4x - 12. Explain your response.

Answer 1

The remainder theorem says $x-c$ is a factor of a polynomial $p(x)$ if $p(c)=0$. So all you need to do is check the value of $x^3+7x^2+4x-12$ when $x=-6$. We have

$(-6)^3+7(-6)^2+4(-6)-12=0$

so $x+6$ is indeed a factor.