Question

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

• A. $5$
• B. $3$
• C. $1$
• D. $6$

Answer 1

The correct option is C $1$

$\text{By remainder theorem, we know that}\text{if a polynomial f(x) is divided by}\text{(x - a), the remainder obtained is f(a).}$

$\text{Using remainder theorem, the}\text{remainder when}p\left(x\right)\text{is divided by}(x+1)\text{is}p(-1).$

$p(-1)=(-1{)}^{100}-(-1{)}^{97}+(-1{)}^{3}p(-1)=1-(-1)-1=1$