Question

Find the value of $t$ for which the polynomial,
$p\left(x\right)=x^3+3x^2+2x+t$ gives $3$ as remainder when divided by $x-1$.

Answer 1

The remainder when $p\left(x\right)$ is divided by $(x-1)$ is $p\left(1\right)$.
(1 Mark)
The remainder is given to be equal to 3.
Therefore $p\left(1\right)=3$. (1 Mark)

$\Rightarrow p\left(x\right)=x³+3x²+2x+t$
$\Rightarrow \left(p\right(1)=(1)³+3\times (1)²+2\times (1)+t$
$\Rightarrow p\left(1\right)=1+3+2+t$
$\Rightarrow 3=6+t$
$\Rightarrow t=-3$ (1 Mark)