Exercise 3.7: Division of Polynomials

Exercise 3.7: Division of Polynomials

1. Find the quotient and remainder of the following.

(i) (4x³ + 6x² – 23x +18) ÷ (x+3)

(ii) (8y³ – 16y² + 16y –15) ÷ (2y–1)

(iii) (8x³ – 1) ÷ (2x–1)

(iv) (–18z + 14z² + 24z³ +18) ÷ (3z+4)

2. The area of a rectangle is x² + 7x + 12. If its breadth is (x+3), then find its length.

3. The base of a parallelogram is (5x+4). Find its height, if the area is 25x²–16.

4. The sum of (x+5) observations is (x³+125). Find the mean of the observations.

5. Find the quotient and remainder for the following using synthetic division:

(i) (x³ + x² −7x − 3) ÷(x − 3) (ii) (x ³ + 2x² −x − 4) ÷(x + 2)

(iii) (3x ³ − 2x² + 7x − 5) ÷(x + 3) (iv) (8x ⁴ − 2x² + 6x + 5) ÷(4x +1)

6. If the quotient obtained on dividing (8x ⁴ − 2x² + 6x −7) by (2x +1) is (4x ³ + px ² −qx + 3) , then find p, q and also the remainder.

7. If the quotient obtained on dividing 3x³ + 11x² + 34x +106 by x − 3 is 3x² + ax +b , then find a, b and also the remainder.