## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.4

Question 1.

Divide:

(i) – 39pq^{2}r^{5} by – 24p^{3}q^{3}r

(ii) –\(\frac{3}{4}\)a^{2}b^{3} by \(\frac{6}{7}\)a^{3}b^{2}

Solution:

Question 2.

Divide:

(i) 9x^{4} – 8x^{3} – 12x + 3 by 3x

(ii) 14p^{2}q^{3} – 32p^{3}q^{2} + 15pq^{2} – 22p + 18q by – 2p^{2}q.

Solution:

Question 3.

Divide:

(i) 6x^{2} + 13x + 5 by 2x + 1

(ii) 1 + y^{3} by 1 + y

(iii) 5 + x – 2x^{2} by x + 1

(iv) x^{3} – 6x^{2} + 12x – 8 by x – 2

Solution:

∴ Quotient = 3x + 5

and remainder = 0

∴ Quotient = y^{2} – y + 1

and remainder = 0

(iii) Arranging the terms of dividend in descending order

of powers of x and then dividing, we get

∴ Quotient = – 2x + 3 and remainder = 2

(iv) x^{3} – 6x^{2} + 12x – 8 by x – 2

Quotient = x^{2} – 4x + 4 and remainder = 0

Question 4.

Divide:

(i) 6x^{3} + x^{2} – 26x – 25 by 3x – 7

(ii) m^{3} – 6m^{2} + 7 by m – 1

Solution:

(i)

∴ Quotient = 2x^{2} + 5x + 3 and remainder = – 4

∴ Quotient = m^{2} – 5m – 5 and remainder = 2.

Question 5.

Divide:

(i) a^{3} + 2a^{2} + 2a + 1 by + a^{2} + a + 1

(ii) 12x^{3} – 17x^{2} + 26x – 18 by 3x^{2} – 2x + 5

Solution:

∴ Quotient = a + 1 and remainder = 0.

(ii) 12x^{3} – 17x^{2} + 26x – 18 by 3x^{2} – 2x + 5

∴ Quotient = 4x – 3 and remainder = -3

Question 6.

If the area of a rectangle is 8x^{2} – 45y^{2} + 18xy and one of its sides is 4x + 15y, find the length of adjacent side.

Solution:

Area of rectangle = 8x^{2} – 45y^{2} + 18xy

One side = 4x + 15y

∴ Second (adjacent) side