Question

Help plz
Use synthetic division and the Remainder Theorem to find P(a). P(x)=x^4+10x^3+8x^2+4x+10; a=2

Answer 1

Synthetic division yields
\[\begin{array}{r|rrrrr}
2&1&10&8&4&10\\
&&2&24&64&136\\
\hline
&1&12&32&68&146
\end{array}\]which is to say
\[\frac{P(x)}{x-2}=x^3+12x^2+32x+68+\underbrace{\frac{146}{x-2}}_{\text{remainder}}\]The polynomial remainder theorem says that \(P(2)\) is the value of the remainder, so \(P(2)=146\).