FINDING QUOTIENT AND REMAINDER OF POLYNOMIALS WORKSHEET

(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)        Solution

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

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

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

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

(i)  (x³ + x² - 7x - 3) ÷ (x - 3)

(ii)  (x³ + 2x² - x - 4) ÷ (x + 2)

(iii)  (3x³ - 2x² + 7x - 5) ÷ (x + 3)

(iv)  (8x⁴ - 2x² + 6x + 5) ÷ (4x + 1)

(v)  (8x⁴ - 2x² + 6x + 5) ÷ (4x + 1)              Solution

(6)  If the quotient obtained on dividing (8x⁴ - 2x² + 6x - 7) by (2x + 1) is (4x³ + px² - qx + 3) then find p, q and also the remainder.         Solution

(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.          Solution

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