Question

Divide p(x) = x4 + 6x3 + 7x2 − 6x − 8 by x + 4 and by x − 3 to find the remainder in each case. Make sure to use the remainder theorem.

Answer 1

The remainder theorem says that dividing a polynomial $p(x)$ by $x-c$ leaves a remainder of $p(c)$. Here, $c=-4$, then $c=3$.

$p(-4)=0$

$p(3)=280$