Question

Divide:
(i) 5m³ − 30m² + 45m by 5m
(ii) 8x²y² − 6xy² + 10x²y³ by 2xy
(iii) 9x²y − 6xy + 12xy² by − 3xy
(iv) 12x⁴ + 8x³ − 6x² by − 2x²

Answer 1

(i) 5m³ − 30m² + 45m by 5m

$$\begin{gathered} (5m^3-30m^2+45m)÷5m \\ \Rightarrow \frac{5m^3}{5m}-\frac{30m^2}{5m}+\frac{45m}{5m} \\ \Rightarrow m^2-6m+9 \end{gathered}$$

Therefore, the quotient is m² − 6m + 9.

(ii) 8x²y² − 6xy² + 10x²y³ by 2xy

$$\begin{gathered} (8x^2{y}^2-6x{y}^2+10x^2{y}^3)÷2xy \\ \Rightarrow \frac{8x^2{y}^2}{2xy}-\frac{6x{y}^2}{2xy}+\frac{10x^2{y}^3}{2xy} \\ \Rightarrow 4xy-3y+5x{y}^2 \end{gathered}$$

Therefore, the quotient is 4xy − 3y + 5xy².

(iii) 9x²y − 6xy + 12xy² by − 3xy

$$\begin{gathered} (9x^{2}y-6xy+12x{y}^2)÷-3xy \\ \Rightarrow \frac{9x^{2}y}{-3xy}-\frac{6xy}{-3xy}+\frac{12x{y}^2}{-3xy} \\ \Rightarrow -3x+2-4y \end{gathered}$$

Therefore, the quotient is −3x + 2 − 4y.

(iv) 12x⁴ + 8x³ − 6x² by − 2x<sup>2

$$\begin{gathered} (12x^4+8x^3-6x^2)÷-2x^2 \\ \Rightarrow \frac{12x^4}{-2x^2}+\frac{8x^3}{-2x^2}-\frac{6x^2}{-2x^2} \\ \Rightarrow -6x \end{gathered}$$2-4x+32</sup>

Therefore the quotient is −6x² − 4x + 3.