Question

Dividing polynomial$x^4-9x^2+9$ by $x^2-3x$, the quotient and the remainder are :

Answer 1

On, Dividing$p\left(x\right)$$=x⁴–9x²+9$by $g\left(x\right)=x²–3x$

$$\begin{gathered} x^2-3x)x^4-9x^2+9(x^2+3x \\ {x}^4-3x^3 \\ \underline{-+} \\ 3x^3-9x^2+9 \\ 3x^3-9x^2 \\ \underline{-+} \\ 9 \end{gathered}$$

We get$q\left(x\right)=x²+3x$ and $r\left(x\right)=9$ ( $q\left(x\right),r\left(x\right)$are quotient and remainder respectively )

Hence, $q\left(x\right)=x²+3x$ and $r\left(x\right)=9$ is the correct answer.