Question

Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder.
$p\left(x\right)=x^4-3x^2+4x+5$
$g\left(x\right)=x^2+1-x$

• A. $q\left(x\right)=x^2+x-3$ and $r\left(x\right)=-8$
• B. $q\left(x\right)=x^2-x+3$ and $r\left(x\right)=8$
• C. $q\left(x\right)=x^2+x-3$ and $r\left(x\right)=8$
• D. $q\left(x\right)=x^2-x-3$ and $r\left(x\right)=-8$

Answer 1

Answer: (C)

$q\left(x\right)=x^2+x-3$ and $r\left(x\right)=8$

$x^2-x+1)x^4-3x^2+4x+5$ ( $x^2+x-3$
$\underset{–}{\underset{-}{}{x}^4\underset{-}{+}{x}^2\underset{+}{-}{x}^3}$
$x^3-4x^2+4x+5$
$\underset{–}{{\underset{-}{x}}^3\underset{+}{-}{x}^2\underset{-}{+}x}$
$-3x^2+3x+5$
$\underset{–}{\underset{+}{-}3x^2\underset{-}{+}3x\underset{+}{-}3}$
$8$
Hence, Quotient=$x^2+x-3$
Remainder=8.