Question

The remainder when the polynomial $p\left(x\right)=x^{100}-x^{97}+x^3$ is divided by $x+1$ is

• A. 1
• B. 22
• C. 3
• D. 4

Answer 1

Answer: (A)

1

Here, $p\left(x\right)=x^{100}-x^{97}+x^3$,

To check the remainder obtained when $p\left(x\right)$ is divided by $x+1$, equate $x+1$ to $0$ and put that value of $x$ in $p\left(x\right)$.

$x+1=0⟹x=-1$

So,

$p(-1)=(-1{)}^{100}-(-1{)}^{97}+(-1{)}^3$
$=1+1-1$
$=1$
So, by the Remainder Theorem $1$ is the remainder when $x^{100}-x^{97}+x^3$ is divided by $x+1$.

Option $A$ is correct.