Question Video: Determining the Degree of an Algebraic Expression Mathematics

Determine the degree of 𝑦⁴ − 7𝑦².


Video Transcript

Determine the degree of 𝑦 to the fourth power minus seven 𝑦 squared.

In this question, we’re asked to find the degree of an algebraic expression. And we can see something interesting about this expression. All of our variables are raised to positive integer values. In other words, this expression is the sum of monomials. So, it’s a polynomial. So, we’re asked to find the degree of a polynomial. To do this, let’s start by recalling what we mean by the degree of a polynomial.

We recall the degree of a polynomial is the greatest sum of the exponents of the variables in any single term. What this means is we look at each individual term, we add together all of the exponents of our variables, and we want to find the biggest value that this gives us. So, let’s start with the first term in our expression, 𝑦 to the fourth power.

In this case, there’s only one variable and its exponent is four, so the degree of 𝑦 to the fourth power is four. Next, let’s look at our second term, negative seven 𝑦 squared. Once again, there’s only one variable, and we can see its exponent. Its exponent is two. So, the degree of negative seven 𝑦 squared is equal to two. And the degree of our polynomial is the biggest of these numbers. Therefore, its degree is four.

And in fact, we can use the exact same method to find the degree of any polynomial with only one variable. Its degree will just be the highest exponent of that variable which appears in our polynomial. Therefore, we were able to show 𝑦 to the fourth power minus seven 𝑦 squared is a fourth-degree polynomial.

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