Class 8 RD Sharma Solutions – Chapter 8 Division Of Algebraic Expressions – Exercise 8.3

Question 1. Divide x + 2x² + 3x⁴ – x⁵ by 2x

Solution:

Here,

(x + 2x² + 3x⁴ – x⁵) / 2x

x/2x + 2x²/2x + 3x⁴/2x – x⁵/2x

By using this formula ⇒ aⁿ/a^m = a^n-m

1/2 x^1-1 + x^2-1 + 3/2 x^4-1 – 1/2 x^5-1

1/2 + x + 3/2 x³ – 1/2 x⁴

Question 2. Divide y⁴ – 3y³ + 1/2y² by 3y

Solution:

Here,

(y⁴ – 3y³ + 1/2y²)/ 3y

y⁴/3y – 3y³/3y + (½)y²/3y

By using this formula ⇒ aⁿ/a^m = a^n-m

1/3 y^4-1 – y^3-1 + 1/6 y^2-1

1/3y³ – y² + 1/6y

Question 3. Divide -4a³ + 4a² + a by 2a

Solution:

Here,

(-4a³ + 4a² + a) / 2a

-4a³/2a + 4a²/2a + a/2a

By using this formula ⇒ aⁿ/a^m = a^n-m

-2a^3-1 + 2a^2-1 + 1/2 a^1-1

-2a² + 2a + 1/2

Question 4. Divide –x⁶ + 2x⁴ + 4x³ + 2x² by √2x²

Solution:

Here,

(–x⁶ + 2x⁴ + 4x³ + 2x²) / √2x²

-x⁶/√2x² + 2x⁴/√2x² + 4x³/√2x² + 2x²/√2x²

By using this formula ⇒ aⁿ/a^m = a^n-m

-1/√2 x^6-2 + 2/√2 x^4-2 + 4/√2 x^3-2 + 2/√2 x^2-2

-1/√2 x⁴ + √2x² + 2√2x + √2

Question 5. Divide -4a³ + 4a² + a by 2a

Solution:

Here,

(-4a³ + 4a² + a) / 2a

-4a³/2a + 4a²/2a + a/2a

By using this formula ⇒ aⁿ/a^m = a^n-m

-2a^3-1 + 2a^2-1 + 1/2a^1-1

-2a² + 2a + 1/2

Question 6. Divide √3a⁴ + 2√3a³ + 3a² – 6a by 3a

Solution:

Here,

(√3a⁴ + 2√3a³ + 3a² – 6a) / 3a

√3a⁴/3a + 2√3a³/3a + 3a²/3a – 6a/3a

By using this formula ⇒ aⁿ/a^m = a^n-m

√3/3 a^4-1 + 2√3/3 a^3-1 + a^2-1 – 2a^1-1

1/√3 a³ + 2/√3 a² + a – 2

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