Question

Divide the polynomial by the binomial. Write your answer in the form: Dividend = divisor × quotient + remainder

(5) 12m² – m – 7; 3m + 2

Answer 1

(12m² – m – 7) ÷ (3m + 2) can be shown as:

$$\begin{gathered} 4m-3 \\ 3m+2\overline{)12m^2-m-17} \\ 12m^2+8m \\ \underline{--} \\ 0-9m-17 \\ -9m-6 \\ \underline{++} \\ \underline{0-11} \end{gathered}$$

Dividend = divisor × quotient + remainder
$\therefore 12m^2-m-17=(3m+2)\left(4m-3\right)-11$