### Question 1. Divide 5x^{3} – 15x^{2} + 25x by 5x

**Solution:**

We have to divide 5x

^{3}– 15x^{2}+ 25x by 5xSo, (5x

^{3}– 15x^{2}+ 25x)/5x5x

^{3}/5x – 15x^{2}/5x + 25x/5xx

^{2}– 3x + 5

### Question 2. Divide 4z^{3} + 6z^{2 }– z by −1/2 z

**Solution:**

We have to divide 4z

^{3}+ 6z^{2}-z by −1/2 zSo, (4z

^{3 }+ 6z^{2 }– z) / (-1/2)z(4z

^{3}/(-1/2)z) + (6z^{2}/(-1/2)z) + (-z/(-1/2)z)(-4 × 2/1)z

^{2}+ (6 × (-2)/1)z + (-1 × (-2/1))-8z

^{2}– 12z +2

### Question 3. Divide 9x^{2}y – 6xy + 12xy^{2} by (−3/2) xy.

**Solution:**

We have to divide 9y – 6xy + 12xy² by (-3/2)xy

So, (9x

^{2}y – 6xy + 12xy^{2}) / (-3/2)xy(9x

^{2}y/(-3/2)xy ) – (6xy/(-3/2)xy) + (12xy^{2}/(-3/2)xy)(9 × (-2/3)x) – (6 × (-2/3)) + (12 × (-2/3))y

-6x -8y +4

### Question 4. Divide 3x^{2}y^{2} + 2x^{2}y + 15xy by 3xy

**Solution:**

We have to divide 3x

^{2}y^{2}+ 2x^{2}y + 15xy by 3xySo, (x

^{2}y^{2}+ 2x^{2}y + 15xy) / 3xy(3x

^{2}y^{2}/3xy) + (2x^{2}y/3xy) + (15xy/3xy)x

^{2}y + (2/3)x +5

### Question 5. Divide x^{2 }+ 7x + 12 by x + 4

**Solution:**

We have to divide x

^{2}+ 7x + 12 by x + 4So by using long division method we get

Quotient = x + 3

Remainder = 0

### Question 6. Divide 4y^{2} + 3y + 1/2 by 2y + 1

**Solution:**

We have to divide 4y

^{2}+ 3y + 12 by 2y + 1So by using long division method we get

Quotient = 2y + 1/2

Remainder = 0

### Question 7. Divide 3x^{3 }+ 4x^{2 }+ 5x + 18 by x + 2

**Solution:**

We have to divide 3x

^{3 }+ 4x^{2}+ 5x + 18 by x + 2-2x

^{2}– 4x + 18So by using long division method we get

Quotient = 3x

^{2}– 2x + 9Remainder = 0

### Question 8. Divide 14x^{2} – 53x + 45 by 7x – 9

**Solution:**

We have to divide 14x

^{2}– 53x + 45 by 7x – 9So by using long division method we get

Quotient = 2x – 5

Remainder = 0

### Question 9. Divide -21 + 71x – 31x^{2} – 24x^{3} by 3 – 8x

**Solution:**

We have to divide -21 + 71x – 31x

^{2 }– 24x^{3}by 3 – 8xSo by using long division method we get

Quotient = 3x

^{2}+ 5x – 7Remainder = 0

### Question 10. Divide 3y^{4} – 3y^{3} – 4y^{2} – 4y by y^{2 }– 2y

**Solution:**

We have to divide 3y

^{4}– 3y^{3}– 4y^{2}– 4y by y^{2 }– 2y2y

^{2}– 4ySo by using long division method we get

Quotient = 3x

^{2}+ 3y + 2Remainder = 0

### Question 11. Divide 2y^{5} + 10y^{4} + 6y^{3 }+ y^{2} + 5y + 3 by 2y^{3} + 1

**Solution:**

We have to divide 2y

^{5}+ 10y^{4}+ 6y^{3}+ y^{2}+ 5y + 3 by 2y^{3 }+ 1So by using long division method we get

Quotient = y

^{2}+ 5y + 3Remainder = 0

### Question 12. Divide x^{4} – 2x^{3} + 2x^{2} + x + 4 by x^{2} + x + 1.

**Solution:**

We have to divide x

^{4}– 2x^{3}+ 2x^{2}+ x + 4 by x^{2}+ x + 14x

^{2}+ 4x + 4So by using long division method we get

Quotient = x

^{2}– 3x + 4Remainder = 0

### Question 13. Divide m^{3} – 14m^{2} + 37m – 26 by m^{2 }– 12m + 13.

**Solution:**

We have to divide m

^{3}– 14m^{2}+ 37m – 26 by m^{2}– 12m + 13-2m

^{2}+ 24m – 26So by using long division method we get

Quotient = m – 2

Remainder = 0

### Question 14. Divide x^{4} + x^{2} + 1 by x^{2} + x + 1

**Solution:**

We have to divide x

^{4 }+ x^{2 }+ 1 by x^{2}+ x + 1So by using long division method we get

Quotient = x

^{2 }– x + 1Remainder = 0

### Question 15. Divide x^{5} + x^{4} + x^{3 }+ x^{2} + x + 1 by x^{3} + 1

**Solution:**

We have to divide x

^{5 }+ x^{4}+ x^{3 }+ x^{2}+ x + 1 by x^{3}+ 1x

^{3 }+ 1So by using long division method we get

Quotient = x

^{2 }+ x + 1Remainder = 0

### Question 16. Divide 14x^{3} – 5x^{2} + 9x – 1 by 2x – 1

**Solution:**

We have to divide 14x

^{3}– 5x^{2}+ 9x – 1 by 2x – 1So by using long division method we get

Quotient = 7x

^{2 }+ x + 5Remainder = 4

### Question 17. Divide 6x^{3 }– x^{2} – 10x – 3 by 2x – 3

**Solution:**

We have to divide 6x

^{3}– x^{2}– 10x – 3 by 2x – 3So by using long division method we get

Quotient = 3x

^{2 }+ 4x + 1Remainder = 0

### Question 18. Divide 6x^{3 }+ 11x^{2} – 39x – 65 by 3x^{2} + 13x + 13

**Solution:**

We have to divide 6x

^{3 }+ 11x^{2}– 39x – 65 by 3x^{2 }+ 13x + 13So by using long division method we get

Quotient = 2x – 5

Remainder = 0