Division of Polynomials Class 8 Maths Chapter 10 Practice Set 10.2 Solutions Maharashtra Board
Std 8 Maths Practice Set 10.2 Chapter 10 Solutions Answers
Division of Polynomials Class 8 Practice Set 10.2 Question 1. Divide and write the quotient and the remainder.
i. (y
2
+ 10y + 24) ÷ (y + 4)
ii. (p
2
+ 7p – 5) ÷ (p + 3)
iii. (3x + 2x
2
+ 4x
3
) ÷ (x – 4)
iv. (2m
3
+ m
2
+ m + 9) ÷ (2m – 1)
v. (3x – 3x
2
– 12 + x
4
+ x
3
) ÷ (2 + x
2
)
vi. (a
4
– a
3
+ a
2
– a + 1) ÷ (a
3
– 2)
vii. (4x
4
– 5x
3
– 7x + 1) ÷ (4x – 1)
Solution:
i. (y
2
+ 10y + 24) ÷ (y + 4)
∴ Quotient = y + 6
Remainder = 0
ii. (p
2
+ 7p – 5) ÷ (p + 3)
∴ Quotient = p + 4
Remainder = -17
iii. (3x + 2x
2
+ 4x
3
) ÷ (x – 4)
Write the dividend in descending order of their indices.
3x + 2x² + 4x³ = 4x³ + 2x² + 3x
∴ Quotient = 4x² + 18x + 75
Remainder = 300
iv. (2m
3
+ m
2
+ m + 9) ÷ (2m – 1)
∴ Quotient = m² + m + 1
Remainder = 10
v. (3x – 3x
2
– 12 + x
4
+ x
3
) ÷ (2 + x
2
)
Write the dividend in descending order of their indices.
(x
4
+ x
3
– 3x
2
+ 3x – 12) ÷ (x
2
+ 2)
∴ Quotient = x² + x – 5
Remainder = x – 2
vi. (a
4
– a
3
+ a
2
– a + 1) ÷ (a
3
– 2)
∴ Quotient = a – 1
Remainder = a² + a – 1
vii. (4x
4
– 5x
3
– 7x + 1) ÷ (4x – 1)
Write the dividend in descending order of their indices.
(4x
4
– 5x
3
– 7x + 1) = (4x
4
– 5x
3
+ 0x
2
– 7x + 1)
∴ Quotient = \(x^{3}-x^{2}-\frac{x}{4}-\frac{29}{16}\)
Remainder = \(\frac { -13 }{ 16 }\)