Divide:
(i) $5 m^{3} - 30 m^{2} + 45 m$ by $5 m$
(ii) $8 x^{2} y^{2} - 6 x y^{2} + 10 x^{2} y^{3}$ by $2 x y$
(iii) $9 x^{2} y - 6 x y + 12 x y^{2}$ by $- 3 x y$
(iv) $12 x^{4} + 8 x^{3} - 6 x^{2}$ by $- 2 x^{2}$

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Solution

(i) $(5 m^{3} - 30 m^{2} + 45 m) \div 5 m = \frac{5 m^{3}}{5 m} - \frac{30 m^{2}}{5 m} + \frac{45 m}{5 m} = m^{2} - 6 m + 9$

(ii) $(8 x^{2} y^{2} - 6 x y^{2} + 10 x^{2} y^{3}) \div 2 x y = \frac{8 x^{2} y^{2}}{2 x y} - \frac{6 x y^{2}}{2 x y} + \frac{10 x^{2} y^{3}}{2 x y} = 4 x y - 3 y + 5 x y^{2}$

(iii) $9 x^{2} y - 6 x y + 12 x y^{2} \div - 3 x y = \frac{9 x^{2} y}{- 3 x y} - \frac{6 x y}{- 3 x y} + \frac{12 x y^{2}}{- 3 x y} = - 3 x + 2 - 4 y$

(iv) $12 x^{4} + 8 x^{3} - 6 x^{2} \div - 2 x^{2} 12 x^{4} + 8 x^{3} - 6 x^{2} = \frac{12 x^{4}}{- 2 x^{2}} + \frac{8 x^{3}}{- 2 x^{2}} - \frac{6 x^{2}}{- 2 x^{2}} = - 6 x^{2} - 4 x + 3$

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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

(i) (5m3−30m2+45m)÷5m=5m35m−30m25m+45m5m=m2−6m+9 (ii) (8x2y2−6xy2+10x2y3)÷2xy=8x2y22xy−6xy22xy+10x2y32xy=4xy−3y+5xy2 (iii) 9x2y−6xy+12xy2÷−3xy=9x2y−3xy−6xy−3xy+12xy2−3xy=−3x+2−4y (iv) 12x4+8x3−6x2÷−2x212x4+8x3−6x2=12x4−2x2+8x3−2x2−6x2−2x2=−6x2−4x+3

Divide:
(i) $5 m^{3} - 30 m^{2} + 45 m$ by $5 m$
(ii) $8 x^{2} y^{2} - 6 x y^{2} + 10 x^{2} y^{3}$ by $2 x y$
(iii) $9 x^{2} y - 6 x y + 12 x y^{2}$ by $- 3 x y$
(iv) $12 x^{4} + 8 x^{3} - 6 x^{2}$ by $- 2 x^{2}$