Question

The polynomial $p\left(x\right)=4x^3+7x^2–5x+t$, when divided by $x+1$ gives $3$ as the remainder.
Find the value of ‘$t$’.

• A. -3
• B. -4
• C. -5
• D. -6

Answer 1

The correct option is C -5

Using remainder theorem, the remainder when $p\left(x\right)$ is divided by $(x+1)$ is $p(-1)$.
The value of the remainder is given as $3$.
The remainder when P(x) is divided by $x+1$ is 3.

$\therefore p(-1)=3$
$⟹4\times {(-1)}^3+7\times {(-1)}^2-5(-1)+t=3$
$4\times -1+7\times 1+5+t=3$
$-4+7+5+t=3$
$t=-5$