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

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

Question 1.
Divide:
(i) – 39pq²r⁵ by – 24p³q³r
(ii) –\(\frac{3}{4}\)a²b³ by \(\frac{6}{7}\)a³b²
Solution:

Question 2.
Divide:
(i) 9x⁴ – 8x³ – 12x + 3 by 3x
(ii) 14p²q³ – 32p³q² + 15pq² – 22p + 18q by – 2p²q.
Solution:

Question 3.
Divide:
(i) 6x² + 13x + 5 by 2x + 1
(ii) 1 + y³ by 1 + y
(iii) 5 + x – 2x² by x + 1
(iv) x³ – 6x² + 12x – 8 by x – 2
Solution:

∴ Quotient = 3x + 5
and remainder = 0

∴ Quotient = y² – 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) x³ – 6x² + 12x – 8 by x – 2

Quotient = x² – 4x + 4 and remainder = 0

Question 4.
Divide:
(i) 6x³ + x² – 26x – 25 by 3x – 7
(ii) m³ – 6m² + 7 by m – 1
Solution:
(i)

∴ Quotient = 2x² + 5x + 3 and remainder = – 4

∴ Quotient = m² – 5m – 5 and remainder = 2.

Question 5.
Divide:
(i) a³ + 2a² + 2a + 1 by + a² + a + 1
(ii) 12x³ – 17x² + 26x – 18 by 3x² – 2x + 5
Solution:

∴ Quotient = a + 1 and remainder = 0.

(ii) 12x³ – 17x² + 26x – 18 by 3x² – 2x + 5

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

Question 6.
If the area of a rectangle is 8x² – 45y² + 18xy and one of its sides is 4x + 15y, find the length of adjacent side.
Solution:
Area of rectangle = 8x² – 45y² + 18xy
One side = 4x + 15y
∴ Second (adjacent) side

ML Aggarwal Class 8 Solutions for ICSE Maths