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

**Question 1. Divide x + 2x**^{2} + 3x^{4} – x^{5} by 2x

^{2}+ 3x

^{4}– x

^{5}by 2x

**Solution:**

Here,

(x + 2x

^{2}+ 3x^{4}– x^{5}) / 2xx/2x + 2x

^{2}/2x + 3x^{4}/2x – x^{5}/2xBy using this formula ⇒ a

^{n}/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 x

^{3}– 1/2 x^{4}

**Question 2. Divide y**^{4} – 3y^{3} + 1/2y^{2} by 3y

^{4}– 3y

^{3}+ 1/2y

^{2}by 3y

**Solution:**

Here,

(y

^{4}– 3y^{3}+ 1/2y^{2})/ 3yy

^{4}/3y – 3y^{3}/3y + (½)y^{2}/3yBy using this formula ⇒ a

^{n}/a^{m}= a^{n-m}1/3 y

^{4-1}– y^{3-1}+ 1/6 y^{2-1}1/3y

^{3}– y^{2}+ 1/6y

**Question 3. Divide -4a**^{3} + 4a^{2} + a by 2a

^{3}+ 4a

^{2}+ a by 2a

**Solution:**

Here,

(-4a

^{3}+ 4a^{2}+ a) / 2a-4a

^{3}/2a + 4a^{2}/2a + a/2aBy using this formula ⇒ a

^{n}/a^{m}= a^{n-m}-2a

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

^{2}+ 2a + 1/2

**Question 4. Divide –x**^{6} + 2x^{4} + 4x^{3} + 2x^{2} by √2x^{2}

^{6}+ 2x

^{4}+ 4x

^{3}+ 2x

^{2}by √2x

^{2}

**Solution:**

Here,

(–x

^{6}+ 2x^{4}+ 4x^{3}+ 2x^{2}) / √2x^{2}-x

^{6}/√2x^{2}+ 2x^{4}/√2x^{2}+ 4x^{3}/√2x^{2}+ 2x^{2}/√2x^{2}By using this formula ⇒ a

^{n}/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 x

^{4}+ √2x^{2}+ 2√2x + √2

**Question 5. Divide -4a**^{3} + 4a^{2} + a by 2a

^{3}+ 4a

^{2}+ a by 2a

**Solution:**

Here,

(-4a

^{3}+ 4a^{2}+ a) / 2a-4a

^{3}/2a + 4a^{2}/2a + a/2aBy using this formula ⇒ a

^{n}/a^{m}= a^{n-m}-2a

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

^{2}+ 2a + 1/2

**Question 6. Divide √3a**^{4} + 2√3a^{3} + 3a^{2} – 6a by 3a

^{4}+ 2√3a

^{3}+ 3a

^{2}– 6a by 3a

**Solution:**

Here,

(√3a

^{4}+ 2√3a^{3}+ 3a^{2}– 6a) / 3a√3a

^{4}/3a + 2√3a^{3}/3a + 3a^{2}/3a – 6a/3aBy using this formula ⇒ a

^{n}/a^{m}= a^{n-m}√3/3 a

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

^{3}+ 2/√3 a^{2}+ a – 2

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