Question

Divide $x^3-6x^2+11x-6$ by $x-2$ and verify the division algorithm

Answer 1

Let $f\left(x\right)=x^3-6x^2+11x-6$

and $p\left(x\right)=x-2$

Dividing $f\left(x\right)$ by $p\left(x\right)$ we get

Quotient $q\left(x\right)=x^2-4x+3$ and Remainder $r\left(x\right)=0$

$p\left(x\right)q\left(x\right)=(x-2)(x^2-4x+3)p\left(x\right)q\left(x\right)=x^3-4x^2+3x-2x^2+8x-6p\left(x\right)q\left(x\right)=x^3-6x^2+11x-6$

$\Rightarrow p\left(x\right)q\left(x\right)=f\left(x\right)$

$\Rightarrow p\left(x\right)q\left(x\right)+0=f\left(x\right)$

$\Rightarrow p\left(x\right)q\left(x\right)+r\left(x\right)=f\left(x\right)$

Hence division algorithm verified.