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# 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^{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}

**Solution:**

We will find out factors of the algebraic expression and then cancel out common factors of the numerator.

(i) (5x^{2} - 6x) ÷ 3x

(5x^{2} - 6x) can be written as x(5x - 6)

Then, (5x^{2} - 6x) ÷ 3x = x(5x - 6) / 3x

= (5x - 6) / 3

(ii) (3y^{8} - 4y^{6} + 5y^{4}) ÷ y^{4}

(3y^{8} - 4y^{6} + 5y^{4}) can be written as y^{4}(3y^{4} - 4y^{2} + 5)

Then, (3y^{8} - 4y^{6} + 5y^{4}) ÷ y^{4 }= y^{4}(3y^{4} - 4y^{2} + 5) / 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}

8(x^{3}y^{2}z^{2} + x^{2}y^{3}z^{2} + x^{2}y^{2}z^{3}) can be written as 8x^{2}y^{2}z^{2}(x + y + z)

Then, 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 }= 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

(x^{3} + 2x^{2} + 3x) can be written as x(x^{2} + 2x + 3)

Then, (x^{3} + 2x^{2} + 3x) ÷ 2x = x(x^{2} + 2x + 3) / 2x

= (x^{2} + 2x + 3) / 2

(v) (p^{3}q^{6} - p^{6}q^{3}) ÷ p^{3}q^{3}

(p^{3}q^{6} - p^{6}q^{3}) can be written as p^{3}q^{3} (q^{3} - p^{3})

Then, (p^{3}q^{6} - p^{6}q^{3}) ÷ p^{3}q^{3}= p^{3}q^{3} (q^{3} - p^{3}) / p^{3}q^{3}

= q^{3} - p^{3}

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 14

**Video Solution:**

## Divide the given polynomial by the given monomial. (i) (5x² - 6x) ÷ 3x (ii) (3y⁸ - 4y⁶ + 5y⁴) ÷ y⁴^{ }(iii) 8(x³y²z² + x²y³z² + x²y²z³) ÷ 4x²y²z²^{ }(iv) (x³ + 2x² + 3x) ÷ 2x (v) (p³q⁶ - p⁶q³) ÷ p³q³

Class 8 Maths NCERT Solutions Chapter 14 Exercise 14.3 Question 2

**Summary:**

The given polynomial is divided 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} and the results are (i) (5x - 6) / 3 (ii) 3y^{4} - 4y^{2} + 5 (iii) 2(x + y + z) (iv)(x^{2} + 2x + 3) / 2 (v) q^{3} - p^{3}

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