Question

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

f(x) = $2x^4-6x^3+2x^2-x+2$, g(x) = x + 2

Answer 1

f(x) = $2x^4-6x^3+2x^2$ -x + 2, g(x) = x + 2

$\therefore$ x + 2 = 0 $\Rightarrow$ x = - 2

$\therefore$ Remainder = f(-2) = $2(-2{)}^4-6(-2{)}^3+2(-2{)}^2$ - (-2)+2

= 2$\times$ 16 - 6$\times$ (-8)+2$\times$ 4+2+2

= 32 + 48 + 8 + 2 + 2 + = 92

$\therefore$ Remainder = 92