Finding Quotient and Remainder of Polynomials Worksheet
Here we are going to see some practice questions on finding quotient and remainder using long division and synthetic division.
(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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