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.