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# 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:$$(p^3q^6 – p^6q^3 – p^6q^3) ÷ p^3q^3$$

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

$$=q^3-p^3$$