Question

Divide the trinomial by the monomial. Write the answer in the form: Dividend = divisor × quotient + remainder.

(1) 6y² – 18y + 7; 3y
(2) (x⁴ – x³ + x²) ; x²

Answer 1

(1) 6y² – 18y + 7 ÷ 3y can be shown as:

$$\begin{gathered} 2y-6 \\ 3y\overline{)6y^2-18y+7} \\ \underline{-6y^2} \\ 0-18y \\ -18y \\ \underline{+} \\ \underline{0+7} \end{gathered}$$

Dividend = divisor × quotient + remainder
∴ 6y² – 18y + 7 = 3y (2y – 6) + 7

(2) x⁴ – x³ + x² ÷ x² can be shown as:

$$\begin{gathered} x^2-x+1 \\ {x}^2\overline{)x^4-x^3+x^2} \\ \underline{-x^4} \\ 0-x^3 \\ \underline{+-x^3} \\ 0+x^2 \\ \underline{-x^2} \\ \underline{0} \end{gathered}$$

Dividend = divisor × quotient + remainder

$\therefore x^4-x^3+x^2=x^2\left(x^2-x+1\right)+0$