Question

If a polynomial $f\left(x\right)$ is divided by $x-a$, then remainder is

• A. $f\left(0\right)$
• B. $f\left(a\right)$
• C. $f(-a)$
• D. $f\left(a\right)-f\left(0\right)$

Answer 1

The correct option is B $f\left(a\right)$

$f\left(x\right)=(x-a)q\left(x\right)+r\left(x\right)$

where, $q\left(x\right)$ is the quotient when $f\left(x\right)$ is divided by $(x-a)$ and $r\left(x\right)$ is the remainder.

The remainder theorem states that we can write the polynomial in terms of the divisor, and then evaluate the polynomial

For, $x=a$

$f\left(a\right)=0\times q\left(a\right)+r\left(a\right)$

$f\left(a\right)=r\left(a\right)$

Hence, the remainder is $f\left(a\right)$.