Question

What is the remainder when $3x^4-4x^2+8x-1$ is divided by $x-2$ ?

Answer 1

Given, $f\left(x\right)=3x^4-4x^2+8x-1$.

Here, $f\left(x\right)$ is divided by $(x-2)$.

Now, according to the remainder theorem, when $f\left(x\right)$ is divided by $(x-2)$, then the remainder is $f\left(2\right)$. {$\because x-2=0\to x=2$

Then,

$f\left(2\right)=3(2{)}^4-4(2{)}^2+8\left(2\right)-1$

$=3\left(16\right)-4\left(4\right)+16-1$

$=48-16+16-1$

$=47$.

Hence, the remainder obtained is $47$.