If fourth degree polynomial is divided by a quadratic polynomial,

Here $f(x)$ represent dividend and $g(x)$ represent divisor.

$g(x)=$ quadratic polynomial

$g(x)=a x^{2}+b x+c$

Therefore degree of $(f(x))=4$

Degree of $(g(x))=2$

The quotient $\mathrm{q}(\mathrm{x})$ is of degree $2(=4-2)$

The remainder $r(x)$ is of degree 1 or less.

Hence, the degree of the remainder is equal to 1 or less than 1