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

Answer 1

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

We know that,

Remainder theorem formula is: $p\left(x\right)=(x-c)q\left(x\right)+r\left(x\right)$

$p\left(x\right)-(x-c)q\left(x\right)=r\left(x\right)$

So, using g(x)

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

$\therefore$ Remainder $=f\left(x\right)-(x-2)$

$=x^4-3x^2+4-(x-2)$

$=(2{)}^4-3(2{)}^2+4$

$=16-12+4$

$=20-12$

$=8$

Now, verify using actual division:

$\therefore$ Remainder = 8