Question

The degree of the quotient when $6x^3+3x$ is divided by 3x is ___.
The degree of a polynomial is the highest exponent of the variable.

Answer 1

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