Question

When the expression 3x³+px²+qx+8 is divided by x²-3x+2,the remainder is 5x+6.Find the value of p and of q.

Answer 1

Answer:

(3x³ + px² + qx + 8)/(x² - 3x + 2) = f(x) + (5x + 6)/(x² - 3x + 2)

=> 3x³ + px² + qx + 8 = f(x)(x² - 3x + 2) + 5x + 6

i.e. 3x³ + px² + qx + 8 = f(x)(x - 1)(x - 2) + 5x + 6

When x = 1 we have:

3 + p + q + 8 = 5 + 6

=> p + q = 0....(1)

When x = 2 we have:

24 + 4p + 2q + 8 = 10 + 6

=> 4p + 2q = -16

i.e. 2p + q = -8...(2)

(2) - (1) => p = -8, hence q = 8