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 $(x–1)$.

• A. -2
• B. -3
• C. -4
• D. -5

Answer 1

The correct option is B -3

Using remainder theorem, the remainder when $p\left(x\right)$ is divided by $(x-1)$ is $p\left(1\right)$.
The remainder is given to be equal to 3.
$\therefore p\left(1\right)=3$
${\left(1\right)}^3+3\times {\left(1\right)}^2+2\left(1\right)+t=3$
$1+3+2+t=3$
$t=-3$