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) = $4x^4-3x^3-2x^2+x-7$, g(x) = x - 1

Answer 1

f(x) = $4x^4-3x^3-2x^2$ + x-7, g(x) = x - 1

$therefore$ x - 1 = 0 $\Rightarrow$ x = 1

$\therefore$ Remainder = f(1) = $4(1{)}^4-3(1{)}^3-2(1{)}^2$ + 1-7

=$4\times 1-3\times 1-2\times$ 1 + 1 - 7

= 4 - 3 - 2 + 1 - 7 = 5 - 12 = - 7

$\therefore$ Remainder = - 7