Question

Divide the polynomial by the given monomial
(i) $(5x^2-6x)÷3x$
(ii) $(3y^8-4y^6+5y^4)÷y^4$
(iii) $8(x^3{y}^2{z}^2+x^2{y}^3{z}^2+x^2{y}^2{z}^3)÷4x^2{y}^2{z}^2$
(iv) $(x^3+2x^2+3x)÷2x$
(v) $(p^3{q}^6-p^6{q}^3)÷p^3{q}^3$

Answer 1

(i) $(5x^2-6x)÷3x$

$=\frac{5x^2-6x}{3x}$

$=\frac{x(5x-6)}{3x}$

$=\frac{1}{3}(5x-6)$

(ii) $(3y^8-4y^6+5y^4)÷y^4$

$=\frac{3y^8-4y^6+5y^4}{y^4}$

$=\frac{y^4(3y^4-4y^2+5y)}{y^4}$

$=3y^4-4y^2+5$

(iii) $8(x^3{y}^2{z}^2+x^2{y}^3{z}^2+x^2{y}^2{z}^3)÷4x^2{y}^2{z}^2$

$=\frac{8(x^3{y}^2{z}^2+x^2{y}^3{z}^2+x^2{y}^2{z}^3)}{4x^2{y}^2{z}^2}$

$=\frac{8x^2{y}^2{z}^2(x+y+z)}{4x^2{y}^2{z}^2}$

$=2(x+y+z)$

(iv) $(x^3+2x^2+3x)÷2x$

$=\frac{x^3+2x^2+3x}{2x}$

$=\frac{x(x^2+2x+3)}{2x}$

$=\frac{1}{2}(x^2+2x+3)$

(v) $(p^3{q}^6-p^6{q}^3)÷p^3{q}^3$

$=\frac{p^3{q}^6-p^6{q}^3}{p^3{q}^3}$

$=\frac{p^3{q}^3(q^3-p^3)}{p^3{q}^3}$

$=q^3-p^3$