Question

The degree of the quotient when $6x^3+3x$ is divided by $3x$ is ___

Answer 1

First factorize the dividend:
$6x^3+3x$ = $6\times x\times x\times x+3\times x=3\times x(2x^2+1)$
Now, $\frac{6\left(x^3\right)+3x}{3x}$ = $\frac{3x\left(2\right(x^2)+1)}{3x}$= $(2x^2+1)$
So, the degree of the quotient, $2x^2+1$, is 2.