Maharashtra Board Class 8 Maths Chapter 10 Division of Polynomials Set 10.1 Solutions

Question 1. Divide and write the quotient and the remainder.

(i) 21m² ÷ 7m
(ii) 40a³ ÷ (-10a)
(iii) (- 48p⁴) ÷ (- 9p²)
(iv) 40m⁵ ÷ 30m³
(v) (5x³ – 3x²) ÷ x²
(vi) (8p³ - 4p²) ÷ 2p²
(vii) (2y³ + 4y² + 3 ) ÷ 2y²
(viii) (21x⁴ – 14x² + 7x) ÷ 7x³
(ix) (6x⁵ – 4x⁴ + 8x³ + 2x²) ÷ 2x²
(x) (25m² – 15m³ + 10m + 8) ÷ 5m³
Answer: Solution:
(i) 21m² ÷ 7m
3m
7m)21m²
21m²
----
0
Explanation:
7m x 3m = 21m²
∴ Quotient = 3m
Remainder = 0
(ii) 40a³ ÷ (-10a)
-4a²
-10a)40a³
40a³
----
0
Explanation:
-10a x -4a² = 40a³
∴ Quotient = -4a²
Remainder = 0
(iii) (- 48p⁴) ÷ (- 9p²)
16/3 p²
-9p²)-48p⁴
-48p⁴
+
----
0
Explanation:
-9p² x 48p⁴/9p² = -48p⁴
-9p² x 16/3 p² = -48p⁴
∴ Quotient = 16/3 p²
Remainder = 0
(iv) 40m⁵ ÷ 30m³
16/3 P
-9p²)-48p⁴
-48p⁴
+
----
0
Explanation:
-9p² x 48p⁴/9p² = -48p⁴
-9p² x 16/3 p² = -48p⁴
∴ Quotient = 4/3 m²
Remainder = 0
(v) (5x³ – 3x²) ÷ x²
5x-3
x²) 5x³-3x²
5x³
----
0-3x²
-3x²
+
----
0
Explanation:
i. x² x 5x = 5x³
ii. x² x -3 = -3x²
∴ Quotient = 5x - 3
Remainder = 0
(vi) (8p³ – 4p²) ÷ 2p²
4p-2
2p²)8p³-4p²
8p³
----
0-4p²
-4p²
+
----
0
Explanation:
i. 2p² x 4p = 8p³
ii. 2p² x -2 = -4p²
∴ Quotient = 4p - 2
Remainder = 0
(vii) (2y³ + 4y² + 3) ÷ 2y²
y + 2
2y²) 2y³ + 4y² + 3
2y³
----
0 + 4y² + 3
4y²
----
0 + 3
Explanation:
i. 2y² x y = 2y³
ii. 2y² x 2 = 4y²
∴ Quotient = y + 2
Remainder = 3
(viii) (21x⁴ – 14x² + 7x) ÷ 7x³
3x
7x)21x⁴-14x²+7x
21x⁴
----
0-14x²+7x
Explanation:
7x³ x 3x = 21x⁴
∴ Quotient = 3x
Remainder = -14x² + 7x
(ix) (6x⁵ – 4x⁴ + 8x³ + 2x²) ÷ 2x²
3x³-2x² + 4x + 1
2x²) 6x⁵ - 4x⁴ + 8x³ + 2x²
6x⁵
----
0 - 4x⁴ + 8x³ + 2x²
-4x⁴
+
----
0 + 8x³ + 2x²
8x³
----
0 + 2x²
2x²
----
0
Explanation:
i. 2x² x 3x³ = 6x⁵
ii. 2x² x -2x² = -4x⁴
iii. 2x² x 4x = 8x³
iv. 2x² x 1 = 2x²
∴ Quotient = 3x³ – 2x² + 4x + 1
Remainder = 0
(x) (25m² – 15m³ + 10m + 8) ÷ 5m³
5m - 3
5m³) 25m⁴ -15m³ +10m +8
25m⁴
----
0 -15m³ +10m +8
-15m³
+
----
0 +10m +8
Explanation:
i. 5m³ x 5m = 25m⁴
ii. 5m³ x -3 = -15m³
∴ Quotient = 5m - 3
Remainder = 10m + 8 In simple words: This question involves performing polynomial long division for various expressions. Each part demonstrates the step-by-step process of dividing a polynomial by a monomial or another polynomial, identifying the quotient and the remainder.

🎯 Exam Tip: Pay close attention to the signs and exponents during subtraction and multiplication steps in polynomial division. Errors often occur from minor calculation mistakes or incorrect handling of negative terms.

Maharashtra Board Class 8 Maths Chapter 10 Division Of Polynomials Practice Set 10.1 Intext Questions And Activities

Question 1. Fill in the blanks in the following examples. (Textbook pg. no. 61)
1. 2a + 3a = _
2. 7b-4b = _
3. 3p x p² = _
4. 5m² x 3m² = _
5. (2x + 5y) x 3/x = _
6. (3x² + 4y) × (2x + 3y) = _
Answer: Solution:
1. 2a + 3a = 5a
2. 7b-4b = 3b
3. 3p x p² = 3p³
4. 5m² x 3m² = 15m⁴
5. (2x + 5y) x 3/x = 6 + 15y/x
6. (3x² + 4y) × (2x + 3y) = 6x³ + 9x²y + 8xy + 12y² In simple words: This section focuses on fundamental polynomial operations, including addition, subtraction, and multiplication, to reinforce basic algebraic manipulation skills required for higher-level topics.

🎯 Exam Tip: Mastering basic algebraic operations is crucial. Ensure you understand how to combine like terms, and apply exponent rules correctly during multiplication to avoid errors in more complex problems.