# Division Of Polynomials

##### Class 8th Mathematics (new) MHB Solution

##### Class 8^{th} Mathematics (new) MHB Solution

**Practice Set 10.1**- 21m2 ÷ 7m Divide. Write the quotient and the remainder.
- 40a3 ÷ (-10a) Divide. Write the quotient and the remainder.
- (-48p4) ÷ (-9p2) Divide. Write the quotient and the remainder.
- 40m5 ÷ 30m3 Divide. Write the quotient and the remainder.
- (5x3 - 3x2) ÷ x2 Divide. Write the quotient and the remainder.
- (8p3 - 4p2) ÷ 2p2 Divide. Write the quotient and the remainder.
- (2y3 + 4y2 + 3) ÷ 2y2 Divide. Write the quotient and the remainder.…
- (21x4 - 14x2 + 7x) ÷ 7x3 Divide. Write the quotient and the remainder.…
- (6x5 - 4x4 + 8x3 + 2x2) ÷ 2x2 Divide. Write the quotient and the remainder.…
- (25m4 - 15m3 + 10m + 8) ÷ 5m3 Divide. Write the quotient and the remainder.…

**Practice Set 10.2**- (y2 + 10y + 24) ÷ (y + 4) Divide and write the quotient and the remainder.…
- (p2 + 7p - 5) ÷ (p + 3) Divide and write the quotient and the remainder.…
- (3x + 2x2 + 4x3) ÷ (x - 4) Divide and write the quotient and the remainder.…
- (2m3 + m2 + m + 9) ÷ (2m - 1) Divide and write the quotient and the remainder.…
- (3x - 3x2 - 12 + x4 + x3) ÷ (2 + x2) Divide and write the quotient and the remainder.…
- (6*)(a4 - a3 + a2 - a + 1) ÷ (a3 - 2) Divide and write the quotient and the remainder.…
- (7*)(4x4 - 5x3 - 7x + 1) ÷ (4x - 1) Divide and write the quotient and the remainder.…

**Practice Set 10.1**

- 21m2 ÷ 7m Divide. Write the quotient and the remainder.
- 40a3 ÷ (-10a) Divide. Write the quotient and the remainder.
- (-48p4) ÷ (-9p2) Divide. Write the quotient and the remainder.
- 40m5 ÷ 30m3 Divide. Write the quotient and the remainder.
- (5x3 - 3x2) ÷ x2 Divide. Write the quotient and the remainder.
- (8p3 - 4p2) ÷ 2p2 Divide. Write the quotient and the remainder.
- (2y3 + 4y2 + 3) ÷ 2y2 Divide. Write the quotient and the remainder.…
- (21x4 - 14x2 + 7x) ÷ 7x3 Divide. Write the quotient and the remainder.…
- (6x5 - 4x4 + 8x3 + 2x2) ÷ 2x2 Divide. Write the quotient and the remainder.…
- (25m4 - 15m3 + 10m + 8) ÷ 5m3 Divide. Write the quotient and the remainder.…

**Practice Set 10.2**

- (y2 + 10y + 24) ÷ (y + 4) Divide and write the quotient and the remainder.…
- (p2 + 7p - 5) ÷ (p + 3) Divide and write the quotient and the remainder.…
- (3x + 2x2 + 4x3) ÷ (x - 4) Divide and write the quotient and the remainder.…
- (2m3 + m2 + m + 9) ÷ (2m - 1) Divide and write the quotient and the remainder.…
- (3x - 3x2 - 12 + x4 + x3) ÷ (2 + x2) Divide and write the quotient and the remainder.…
- (6*)(a4 - a3 + a2 - a + 1) ÷ (a3 - 2) Divide and write the quotient and the remainder.…
- (7*)(4x4 - 5x3 - 7x + 1) ÷ (4x - 1) Divide and write the quotient and the remainder.…

###### Practice Set 10.1

**Question 1.**Divide. Write the quotient and the remainder.

21m^{2} ÷ 7m

**Answer:**

Therefore, quotient = 3m, remainder = 0.

**Question 2.**Divide. Write the quotient and the remainder.

40a^{3} ÷ (-10a)

**Answer:**

Therefore, quotient = -4a^{2}, remainder = 0.

**Question 3.**Divide. Write the quotient and the remainder.

(-48p^{4}) ÷ (-9p^{2})

**Answer:**

Therefore, quotientremainder

**Question 4.**Divide. Write the quotient and the remainder.

40m^{5} ÷ 30m^{3}

**Answer:**

Therefore, quotient, remainder

**Question 5.**Divide. Write the quotient and the remainder.

(5x^{3} - 3x^{2}) ÷ x^{2}

**Answer:**

Therefore, quotient = 5x – 3, remainder = 0.

**Question 6.**Divide. Write the quotient and the remainder.

(8p^{3} - 4p^{2}) ÷ 2p^{2}

**Answer:**

Therefore, quotient = 4p – 2 , remainder = 0.

**Question 7.**Divide. Write the quotient and the remainder.

(2y^{3} + 4y^{2} + 3) ÷ 2y^{2}

**Answer:**

Therefore, quotient = y + 2, remainder = 3.

**Question 8.**Divide. Write the quotient and the remainder.

(21x^{4} - 14x^{2} + 7x) ÷ 7x^{3}

**Answer:**

Therefore, quotient = 3x, remainder = -14x^{2} + 7x.

**Question 9.**Divide. Write the quotient and the remainder.

(6x^{5} - 4x^{4} + 8x^{3} + 2x^{2}) ÷ 2x^{2}

**Answer:**

Therefore, quotient = 3x^{3} – 2x^{2} + 4x + 1, remainder = 0.

**Question 10.**Divide. Write the quotient and the remainder.

(25m^{4} - 15m^{3} + 10m + 8) ÷ 5m^{3}

**Answer:**

Therefore, quotient = 5m – 3 , remainder = 10m + 8.

**Question 1.**

Divide. Write the quotient and the remainder.

21m^{2} ÷ 7m

**Answer:**

Therefore, quotient = 3m, remainder = 0.

**Question 2.**

Divide. Write the quotient and the remainder.

40a^{3} ÷ (-10a)

**Answer:**

Therefore, quotient = -4a^{2}, remainder = 0.

**Question 3.**

Divide. Write the quotient and the remainder.

(-48p^{4}) ÷ (-9p^{2})

**Answer:**

Therefore, quotientremainder

**Question 4.**

Divide. Write the quotient and the remainder.

40m^{5} ÷ 30m^{3}

**Answer:**

Therefore, quotient, remainder

**Question 5.**

Divide. Write the quotient and the remainder.

(5x^{3} - 3x^{2}) ÷ x^{2}

**Answer:**

Therefore, quotient = 5x – 3, remainder = 0.

**Question 6.**

Divide. Write the quotient and the remainder.

(8p^{3} - 4p^{2}) ÷ 2p^{2}

**Answer:**

Therefore, quotient = 4p – 2 , remainder = 0.

**Question 7.**

Divide. Write the quotient and the remainder.

(2y^{3} + 4y^{2} + 3) ÷ 2y^{2}

**Answer:**

Therefore, quotient = y + 2, remainder = 3.

**Question 8.**

Divide. Write the quotient and the remainder.

(21x^{4} - 14x^{2} + 7x) ÷ 7x^{3}

**Answer:**

Therefore, quotient = 3x, remainder = -14x^{2} + 7x.

**Question 9.**

Divide. Write the quotient and the remainder.

(6x^{5} - 4x^{4} + 8x^{3} + 2x^{2}) ÷ 2x^{2}

**Answer:**

Therefore, quotient = 3x^{3} – 2x^{2} + 4x + 1, remainder = 0.

**Question 10.**

Divide. Write the quotient and the remainder.

(25m^{4} - 15m^{3} + 10m + 8) ÷ 5m^{3}

**Answer:**

Therefore, quotient = 5m – 3 , remainder = 10m + 8.

###### Practice Set 10.2

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

(y^{2} + 10y + 24) ÷ (y + 4)

**Answer:**

Therefore, quotient = y + 6 , remainder = 0.

**Question 2.**Divide and write the quotient and the remainder.

(p^{2} + 7p - 5) ÷ (p + 3)

**Answer:**

Therefore, quotient = p + 4 , remainder = -17.

**Question 3.**Divide and write the quotient and the remainder.

(3x + 2x^{2} + 4x^{3}) ÷ (x - 4)

**Answer:**

Therefore, quotient = 4x^{2} + 18x + 75, remainder = 300.

**Question 4.**Divide and write the quotient and the remainder.

(2m^{3} + m^{2} + m + 9) ÷ (2m - 1)

**Answer:**

Therefore, quotient = m^{2} + m + 1, remainder = 10.

**Question 5.**Divide and write the quotient and the remainder.

(3x - 3x^{2} - 12 + x^{4} + x^{3}) ÷ (2 + x^{2})

**Answer:**

Rearranging the terms we get,

Therefore, quotient = x^{2} + x – 5, remainder = x – 2

**Question 6.**Divide and write the quotient and the remainder.

(6*)(a^{4} - a^{3} + a^{2} - a + 1) ÷ (a^{3} - 2)

**Answer:**

Rearranging the terms we get,

Therefore, quotient = a – 1, remainder = a^{2} + a – 1

**Question 7.**Divide and write the quotient and the remainder.

(7*)(4x^{4} - 5x^{3} - 7x + 1) ÷ (4x - 1)

**Answer:**

Factorising the numerator we get,

Therefore, quotientremainder

**Question 1.**

Divide and write the quotient and the remainder.

(y^{2} + 10y + 24) ÷ (y + 4)

**Answer:**

Therefore, quotient = y + 6 , remainder = 0.

**Question 2.**

Divide and write the quotient and the remainder.

(p^{2} + 7p - 5) ÷ (p + 3)

**Answer:**

Therefore, quotient = p + 4 , remainder = -17.

**Question 3.**

Divide and write the quotient and the remainder.

(3x + 2x^{2} + 4x^{3}) ÷ (x - 4)

**Answer:**

Therefore, quotient = 4x^{2} + 18x + 75, remainder = 300.

**Question 4.**

Divide and write the quotient and the remainder.

(2m^{3} + m^{2} + m + 9) ÷ (2m - 1)

**Answer:**

Therefore, quotient = m^{2} + m + 1, remainder = 10.

**Question 5.**

Divide and write the quotient and the remainder.

(3x - 3x^{2} - 12 + x^{4} + x^{3}) ÷ (2 + x^{2})

**Answer:**

Rearranging the terms we get,

Therefore, quotient = x^{2} + x – 5, remainder = x – 2

**Question 6.**

Divide and write the quotient and the remainder.

(6*)(a^{4} - a^{3} + a^{2} - a + 1) ÷ (a^{3} - 2)

**Answer:**

Rearranging the terms we get,

Therefore, quotient = a – 1, remainder = a^{2} + a – 1

**Question 7.**

Divide and write the quotient and the remainder.

(7*)(4x^{4} - 5x^{3} - 7x + 1) ÷ (4x - 1)

**Answer:**

Factorising the numerator we get,

Therefore, quotientremainder