### Video Transcript

What is the degree of the polynomial function 𝑓 of 𝑥 equals two 𝑥 cubed plus three 𝑥 squared plus 𝑥 plus six?

We’ve been given a polynomial function 𝑓 of 𝑥, and we’re looking to find its degree. So, what do we mean when we talk about the degree of a polynomial function? Well, imagine we have our polynomial function, and it’s made up of a number of monomial terms. The degree of the function is the largest exponent of a variable in any one of these terms.

So, let’s observe each of the monomial terms in our function. They are written in descending order. If we look at the final term six, the constant term, that’s equivalent to six 𝑥 to the zeroth power. 𝑥 is equivalent to 𝑥 to the first power. Then we have three 𝑥 squared — the power is two — and two 𝑥 cubed, where the exponent is Three. There’s only one variable in our function; it’s 𝑥. And the largest exponent of 𝑥 here is three.

So, the degree of the polynomial function 𝑓 of 𝑥 is three.