Video: Determining the Degree of a Polynomial Function

Find the degree of the function 𝑓(𝑥) = −3𝑥(−6𝑥 + 10)³.

02:26

Video Transcript

Find the degree of the function 𝑓 𝑥 is equal to negative three 𝑥 multiplied by negative six 𝑥 plus 10 to the power of three.

To solve this problem, first of all, we need to know what is the degree of a function. Well, actually, the degree of a function in this case a polynomial — cause that’s what we’re looking at — is the highest degree of its monomials with nonzero coefficients.

Well, is this useful? What’s a monomial? Well, actually, a monomial is actually an individual term. So actually, this is really useful because it tells us that if we want to find out the degree of our function, what we need to do is find out the highest degree of one of the individual terms.

So if we take a look at our function, so we got 𝑓𝑥 is equal to negative three 𝑥 multiplied by negative six 𝑥 plus 10 all cubed, then we can actually see that if we want to find the highest degree of this function, then we’re actually only concerned with the negative six 𝑥 cubed from the terms that are in the parenthesis. And the reason this is is actually because it’s gonna give us the highest degree from any of those terms.

So therefore, if we’re gonna try and find the highest degree of our function, we just need to multiply negative three 𝑥 by negative six 𝑥 all cubed. So this gonna be equal to negative three 𝑥 multiplied by negative 216 𝑥 cubed. And it’s still negative 216 𝑥 cubed because you’ve got negative six cubed, which is negative 216, and then 𝑥 cubed, which is 𝑥 cubed. And this will give us an answer of 648 𝑥 to the power of four.

We’re not really interested in this 648, which is the coefficient of our 𝑥 to the power of four. However, what it does tell us is that because it’s nonzero, then, okay, we can look at this monomial as the one that we’re looking for for the highest degree.

What we’re really interested in is the power of 𝑥. And we can see in this case that it’s four. So therefore, we can say that the degree of 𝑓𝑥 is equal to negative three 𝑥 multiplied by negative six 𝑥 plus 10 all cubed is equal to four. And that’s because four is the highest degree of any individual term within the function.

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