Question

What is the degree of the remainder atmost, when a fourth degree polynomial is divided by a quadratic polynomial?

• A. $2$
• B. $0$
• C. $4$
• D. $1$

Answer 1

The correct option is D $1$

Here $f\left(x\right)$ represent dividend and $g\left(x\right)$ represent divisor

$g\left(x\right)=$ quadratic polynomial $=a{x}^2+bx+c$

$\therefore deg\left(g\right(x\left)\right)=2$, $deg\left(f\right(x\left)\right)=4$

quotient $q\left(x\right)$ is of degree $=2$ $(=4-2)$

According to the division algorithm, deg$\left(g\right(x\left)\right)$ > deg($r\left(x\right)$) > 0

2 > deg($r\left(x\right)$) > 0

Remainder $R\left(x\right)=$ degree $1$ or less than $1$.