## Chapter 10 Division of Polynomials Set 10.2

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)