Question

.If the polynomial f (x) = px3 + 4x2 + 3x - 4 and g(x) = x3 – 4x + p are divided by (x-3), then the remainder in each case is the same, find the value of p

Answer 1

p = -1.

Explanation:

By the Remainder Theorem the remainder when x- 3 is divided into f(x) is

p(3)^3 + 4(3)^2 + 3(3) - 4 = 27p + 41.

The remainder when x^3 - 4x + 9 is divided by x- 3 = 27 -12 + p = 15 + p.

So 27p + 41 = 15 + p

26p = - 26

p = -1.