Video Transcript
Find the degree of the binomial two 𝑥 squared 𝑦𝑧 raised to the fourth power plus three 𝑥 cubed 𝑧.
In this question, we are asked to find the degree of a given binomial. And we can start by recalling that this is the largest degree of its monomial terms. We can also recall that the degree of a monomial is the sum of the powers of all of its variables. Therefore, the degree of a binomial, or any polynomial, is the largest sum of the powers of the variables in a term.
Let’s start by calculating the degree of the first term. We know that 𝑦 is equal to 𝑦 raised to the first power. So, the sum of the powers of the variables in the first term is two plus one plus four, which is equal to seven. Thus, the first term is a degree seven monomial. In the same way, we can calculate that the degree of the second term is the sum of the powers of the variables in this term, which is four. Finally, the larger of these degrees is the degree of the binomial.
Hence, the given binomial is of degree seven.
