# How do you use synthetic division to find x=2 for P(x) = x^4+x^2+x-6?

Jan 30, 2018

Substitution : $\textcolor{b l u e}{P \left(x\right) = P \left(2\right) = 20}$

Synthetic Division :
Quotient $\textcolor{b r o w n}{Q = {x}^{3} + 2 {x}^{2} + 5 x + 11}$, Remainder color(red)(R = 16/(x-2)

#### Explanation:

$P \left(x\right) = {x}^{4} + {x}^{2} + x - 6$ for $x = 2$

$P \left(x\right) = P \left(2\right) = {2}^{4} + {2}^{2} + 2 - 6 = 20$

$\textcolor{w h i t e}{a a} 2 \textcolor{w h i t e}{a a} | \textcolor{w h i t e}{a a} 1 \textcolor{w h i t e}{a a} 0 \textcolor{w h i t e}{a a} 1 \textcolor{w h i t e}{a a} 1 \textcolor{w h i t e}{a a} - 6$
$\textcolor{w h i t e}{a a a a a a} | \downarrow \textcolor{w h i t e}{a a} 2 \textcolor{w h i t e}{a a} 4 \textcolor{w h i t e}{a} 10 \textcolor{w h i t e}{a a a} 22$
$\textcolor{w h i t e}{a a a a a} - - - - - - - -$
$\textcolor{w h i t e}{a a a a a a a a a} 1 \textcolor{w h i t e}{a a} 2 \textcolor{w h i t e}{a a} 5 \textcolor{w h i t e}{a} 11 \textcolor{w h i t e}{a a a} 16$

Quotient $\textcolor{b r o w n}{Q = {x}^{3} + 2 {x}^{2} + 5 x + 11}$, Remainder color(red)(R = 16/(x-2)