Question

For the polynomial $f\left(x\right)=x^3-6x^2+11x-6$, which of the following is/are true?
(Check using Remainder Theorem)

• A. On dividing $f\left(x\right)$ by $x+1$, the remainder obtained is $-24$
• B. On dividing $f\left(x\right)$ by $x-2$, the remainder obtained is $1$
• C. All of the above
• D. On dividing $f\left(x\right)$ by $x-2$, the remainder obtained is $0$

Answer 1

Answer: (A), (D)

On dividing $f\left(x\right)$ by $x-2$, the remainder obtained is $0$

The given polynomial is $f\left(x\right)=x^3-6x^2+11x-6$.

Remainder Theorem states that if a polynomial $p\left(x\right)$ is divided by $x-a$, then the remainder obtained is $p\left(a\right)$

On dividing $f\left(x\right)$ by $x-2$, the remainder obtained will be:
$f\left(2\right)=2^3-6(2{)}^2+11(2)-6=8-24+22-6=0$

and
On dividing $f\left(x\right)$ by $x+1$, the remainder obtained will be:
$f(-1)=(-1{)}^3-6(-1{)}^2+11(-1)-6=-1-6-11-6=-24$