###### Advertisements

###### Advertisements

**Find the quotient and the remainder when :**a

^{3 }− 5a

^{2}+ 8a + 15 is divided by a + 1. verify your answer.

###### Advertisements

#### Solution

`"a"+1) overline("a"^3-5"a"^2+8"a"+15)("a"^2-6"a"+14`

a^{3} + a^{2 }

− −

−6a^{2} + 8a + 15

−6a2 − 6a

+ +

14a + 15

14a + 14

1

∴ Quotient = a^{2} − 6a + 14 and reminder = 1

**Verification :**

Dividiend = Quotient × Divisor + Reminder

= (a2 − 6a + 14) × (a + 1) + 1

= a^{3} − 6a^{2} + 14a + a^{2} − 6a + 14 + 1

= a^{3} − 5a^{2} + 8a + 15 which is given

#### APPEARS IN

#### RELATED QUESTIONS

**Work out the following divisions:**

10y(6y + 21) ÷ 5(2y + 7)

**Work out the following divisions:**

9x^{2}y^{2}(3z − 24) ÷ 27xy(z − 8)

**Factorise the expression and divide them as directed.**

(5p^{2} − 25p + 20) ÷ (p − 1)

**Factorise the expression and divide them as directed.**

4yz(z^{2} + 6z − 16) ÷ 2y(z + 8)

Find the greatest common factor (GCF/HCF) of the following polynomial:

42x^{2}yz and 63x^{3}y^{2}z^{3}

Find the greatest common factor (GCF/HCF) of the following polynomial:

4a^{2}b^{3}, −12a^{3}b, 18a^{4}b^{3}

Find the greatest common factor (GCF/HCF) of the following polynomial:

6x^{2}y^{2}, 9xy^{3}, 3x^{3}y^{2}

Find the greatest common factor (GCF/HCF) of the following polynomial:

36a^{2}b^{2}c^{4}, 54a^{5}c^{2}, 90a^{4}b^{2}c^{2}

Find the greatest common factor (GCF/HCF) of the following polynomial:

15a^{3}, − 45a^{2}, − 150a

**Divide:** a^{2} + 7a + 12 by a + 4

**Divide:** x^{2} + 3x − 54 by x − 6

**Divide:** 12x^{2} + 7xy − 12y^{2} by 3x + 4y

**Divide:** 4a^{2} + 12ab + 9b^{2} − 25c^{2} by 2a + 3b + 5c

**Divide: **16 + 8x + x^{6} − 8x^{3} − 2x^{4} + x^{2} by x + 4 − x^{3}

**Find the quotient and the remainder when :**

3x^{4} + 6x^{3} − 6x^{2} + 2x − 7 is divided by x − 3. verify your answer.

**Find the quotient and the remainder when :**

6x^{2} + x − 15 is divided by 3x + 5. verify your answer.

The area of a rectangle is x^{3} – 8x + 7 and one of its sides is x – 1. Find the length of the adjacent side.

The product of two numbers-is 16x^{4} – 1. If one number is 2x – 1, find the other.

Divide x^{6} – y^{6} by the product of x^{2} + xy + y^{2} and x – y.

^{4 }– 5x

^{3 }– 24x

^{2}) by 11x(x – 8).