2.Divide the given polynomial by the given monomial,
(i) \((5x^2 – 6x) ÷ 3x\)

(ii) \((3y^8 – 4y^6 + 5y^4) ÷ y^4\)

(iii) \(8(x^3y^2z^2 + x^2y^3z^2 + x^2y^2z^3) ÷ 4x^2y^2z^2\)

(iv) \((x^3 + 2x^2 + 3x) ÷ 2x\)

(v) \((p^3q^6 – p^6q^3 – p^6q^3) ÷ p^3q^3\)

(i)Given: \((5x^2 – 6x) ÷ 3x\)

\(=\frac{5x^2 – 6x}{3x}=\frac{5x^2}{3x}-\frac{6x}{3x}\)

\(=\frac{5}2x-2=\frac{1}3(5x-6)\)

(ii)Given:\((3y^8 – 4y^6 + 5y^4) ÷ y^4\)

\(=\frac{3y^8 – 4y^6 + 5y^4}{y^4}=\frac{3y^8}{y^4}-\frac{4y^6 }{y^4}+\frac{5y^4 }{y^4}\)

\(=3y^4-4y^2+5\)

(iii)Given:\(8(x^3y^2z^2 + x^2y^3z^2 + x^2y^2z^3) ÷ 4x^2y^2z^2\)

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

\(=2(x+y+z)\)

(iv)Given: \((x^3 + 2x^2 + 3x) ÷ 2x\)

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

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

(v)Given:\((p^3q^6 – p^6q^3 – p^6q^3) ÷ p^3q^3\)

\(=\frac{p^3q^6 – p^6q^3 – p^6q^3}{p^3q^3}=\frac{p^3q^3(q^3-p^3)}{p^3q^3}\)

\(=q^3-p^3\)