Question

Two students are analyzing the expression 3x ^ 7 * y ^ 5

Jessica states that the expression is a binomial with a degree of 12. Sam states that the expression is a monomial with a degree of 7.

Is either student correct? Justify your answer.

Please upload a picture of your handwritten work below.

Answer 1

Both students are incorrect.

To determine the degree of an expression, we look at the exponents of the variables.

In the given expression, the variable x has an exponent of 7 and the variable y has an exponent of 5. The degree of the expression is determined by adding the exponents of the variables, so the degree is 7 + 5 = 12.

However, the expression is not a binomial because a binomial consists of two terms separated by addition or subtraction. The expression provided has only one term. Therefore, Jessica's statement is incorrect.

Furthermore, the expression is not a monomial either. A monomial consists of only one term, but this expression has two variables, x and y. Therefore, Sam's statement is incorrect as well.

So, the expression is neither a binomial nor a monomial, and its degree is 12.