(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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