Question

Divide (3x³ − 4x² + 7x − 2) by (x² − x + 2) and verify the division algorithm.

Answer 1

$\begin{array}{l}\text{First, we will write the given polynomials in their standard forms in}\\ \text{decreasing order of degrees and then perform the division as shown below:}\\ \end{array}$



$\begin{array}{l}\therefore \text{Quotient}=(3x-1)\mathrm{and}\text{remainder}=0\\ \Rightarrow (\text{Quotient}\times \text{divisor})+\text{remainder=}(3x-1)\times (x^2-x+2)+0\\ \\ =3x^3-x^2-3x^2+x+6x-2\\ =3x^3-4x^2+7x-2\\ =\text{dividend}\\ \text{Thus,}(\text{quotient}\times \text{divisor})+\text{remainder}=\text{dividend}\\ \text{Hence, the division algorithm is verified}\text{.}\end{array}$