## MP Board Class 8th Maths Solutions Chapter 14 Factorization Ex 14.3

Question 1.

Carry out the following divisions.

(i) 28x^{4} ÷ 56x

(ii) -36y^{3} ÷ 9y^{2}

(iii) 66pq^{2}r^{3} ÷ 11qr^{2}

(iv) 34x^{3}y^{3}z^{3} ÷ 51 xy^{2}z^{3}

(v) 12a^{8}b^{8} ÷ (- 6a^{6}b^{4}).

Solution:

(i) 28x^{4} ÷ 56x

Question 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^{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:

(i) We have

Question 3.

Work out the following divisions.

(i) (10x – 25) ÷ 5

(ii) (10x- 25) ÷ (2x- 5)

(iii) 10y(6y + 21) ÷ 5(2y + 7)

(iv) 9x^{2}y^{2}(3z – 24) ÷ 27xy(z – 8)

(v) 96abc(3a -12)(5b – 30) ÷ 144(a – 4)(b – 6)

Solution:

(i) We have,

(10x – 25) ÷ 5 = \(\frac{10 x-25}{5}\)

= \(\frac{5(2 x-5)}{5}\) = (2x – 5)

(ii) We have,

Question 4.

Divide as directed.

(i) 5(2x + 1 )(3x + 5) ÷ (2x + 1)

(ii) 26xy(x + 5)(y – 4) ÷ 13x(y – 4)

(iii) 52pqr (p + q)(q + r)(r + p) ÷ 104pq(q + r)(r + p)

(iv) 20(y + 4) (y^{2} + 5y + 3) ÷ 5(y + 4)

(v) x(x + 1)(x + 2)(x + 3) ÷ x(x + 1)

Solution:

(i) We have, 5(2x + 1)(3x + 5) ÷ (2x + 1)

Question 5.

Factorise the expressions and divide them as directed.

(i) (y^{2} + 7y + 10) ÷ (y + 5)

(ii) (m^{2} – 14m – 32) ÷ (m + 2)

(iii) (5p^{2} – 25p + 20) ÷ (p – 1)

(iv) 4yz(z^{2} + 6z – 16) ÷ 2y(z + 8)

(v) 5pq(p^{2} – q^{2}) ÷ 2p(p + q)

(vi) 12xy(9x^{2} – 16y^{2}) ÷ 4xy(3x + 4y)

(vii) 39y^{3}(50y^{2} – 98) ÷ 26y^{2}(5y + 7)

Solution:

(i) We have, y^{2} + 7y + 10

= y^{2} + 5y + 2y + 10

= y(y + 5) + 2(y + 5) = (y + 2) (y + 5)