Question

Use remainder theorem to find the remainder when $f\left(x\right)=3x^2+4x-11$ is divided by $(x-1)$.

Answer 1

Given, $f\left(x\right)=3x^2+4x-11$.

Here, $f\left(x\right)$ is divided by $(x-1)$.

Now, according to the remainder theorem, when $f\left(x\right)$ is divided by $(x-1)$, then the remainder is $f\left(1\right)$.

Then,

$f\left(1\right)=3(1{)}^2+4(1)-11$

$=3+4-11=-4$.

Hence, the remainder obtained is $-4$.