Question

Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder.
$p\left(x\right)=x^4-5x+6$
$g\left(x\right)=2-x^2$

• A. $(-x^2-2)$ and $(5x+10)$
• B. $(-x^2-2)$ and $(-5x+10)$
• C. $(-x^2+2)$ and $(-5x+10)$
• D. $(-x^2+2)$ and $(5x+10)$

Answer 1

The correct option is B $(-x^2-2)$ and $(-5x+10)$

$-x^2+2)\overline{x^4-5x+6}$( $-x^2-2$
$\underset{–}{{\underset{-}{x}}^4\underset{+}{-}2x^2}$
$2x^2-5x+6$
$\underset{–}{\underset{-}{2}{x}^2\underset{+}{-}4}$
$-5x+10$
Therefore, quotient=$-x^2-2$ and
Remainder=$-5x+10$