The Degree

The degree of a polynomial in $x$ is the largest exponent of $x$ after the polynomial is simplified. The polynomial $x^{2}+3x+2$ has degree 2, and $5x^{7}-x$ has degree 7.

Simplify any products and collect the like terms before you read the degree. For example, $xx^{2}+x^{3} = x^{3}+x^{3} = 2x^{3}$. The result is a monomial of degree 3.

Standard form lists the terms from the largest exponent down to the smallest. For example, $2+3x+x^{2}$ in standard form is $x^{2}+3x+2$. In standard form, the exponent of the first term is the degree.