Question

When P(x) is divided by x-2 the quotient is Q(x) and the remainder is 5.When Q(x) is divided by x^2+2x+4 the remainder is 2x-3.What is remainder when P(x) is divided by x^3-8

Answer 1

Explanation:

P(x)

= (x - 2)Q¹(x) + 5

= (x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5.

Since x³ - 8 = (x - 2)(x² + 2x + 4),

(x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5

= (x - 2)(x² + 2x + 4)Q²(x) + (x - 2)(2x - 3) + 5

= (x³ - 8)Q²(x) + (2x² - 7x + 11).

Hence when P(x) is divided by (x³ - 8),

the remainder is 2x² - 7x + 11.