Question

Divide (12 − 17x − 5x²) by (3 − 5x) and verify the division algorithm.

Answer 1

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



$\begin{array}{l}\therefore \text{Quotient}=(x+4)\mathrm{and}\text{remainder=0}\\ \text{⇒}(\text{Quotient}\times \text{divisor})+\text{remainder=}(x+4)\times (-5x+3)+0\\ \\ =-5x^2-20x+3x+12\\ =5x^2-17x+12\\ =\text{dividend}\\ \text{Thus,}(\mathrm{q}\text{uotient}\times \text{divisor})+\text{remainder}=\text{dividend}\\ \text{Hence, the division algorithm is verified}\text{.}\end{array}$