Chapter 10 Division of Polynomials Set 10.1
Question 1.
Divide and write the quotient and the remainder.
i. 21m² ÷ 7m
ii. 40a³ ÷ (-10a)
iii. (- 48p^{4}) ÷ (- 9p^{2})
iv. 40m^{5} ÷ 30m^{3}
v. (5x^{3} – 3x^{2}) ÷ x²
vi. (8p^{3} – 4p^{2}) ÷ 2p^{2}
vii. (2y^{3} + 4y^{2} + 3 ) ÷ 2y^{2}
viii. (21x^{4} – 14x^{2} + 7x) ÷ 7x^{3}
ix. (6x^{5} – 4x^{4} + 8x^{3} + 2x^{2}) ÷ 2x^{2}
x. (25m^{4} – 15m^{3} + 10m + 8) ÷ 5m^{3}
Solution:
i. 21m² ÷ 7m
∴ Quotient = 3m
Remainder = 0
ii. 40a³ ÷ (-10a)
∴ Quotient = -4a²
Remainder = 0
iii. (- 48p^{4}) ÷ (- 9p^{2})
∴ Quotient = 16/3 p²
Remainder = 0
iv. 40m^{5} ÷ 30m^{3}
∴ Quotient = 4/3 m²
Remainder = 0
v. (5x^{3} – 3x^{2}) ÷ x²
∴ Quotient = 5x – 3
Remainder = 0
vi. (8p^{3} – 4p^{2}) ÷ 2p^{2}
∴ Quotient = 4p – 2
Remainder = 0
vii. (2y^{3} + 4y^{2} + 3 ) ÷ 2y^{2}
∴ Quotient = y + 2
Remainder = 3
viii. (21x^{4} – 14x^{2} + 7x) ÷ 7x^{3}
∴ Quotient = 3x
Remainder = -14x² + 7x
ix. (6x^{5} – 4x^{4} + 8x^{3} + 2x^{2}) ÷ 2x^{2}
∴ Quotient = 3x³ – 2x² + 4x + 1
Remainder = 0
x. (25m^{4} – 15m^{3} + 10m + 8) ÷ 5m^{3}
∴ Quotient = 5m – 3
Remainder = 10m + 8
Intext Questions and Activities
Question 1.
Fill in the blanks in the following examples. (Textbook pg. no. 61)
- 2a + 3a = __
- 7b – 4b = __
- 3p × p² = __
- 5m² × 3m² = __
- (2x + 5y) × 3x = __
- (3x² + 4y) × (2x + 3y) = __
Solution:
- 2a + 3a = 5a
- 7b – 4b = 3b
- 3p × p² = 3p³
- 5m² × 3m² = 15m^{4}
- (2x + 5y) × 3x = 6+15y/x
- (3x² + 4y) × (2x + 3y) = 6x³ + 9x²y + 8xy + 12y²