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.
Sam is correct.
A binomial is an algebraic expression with two unlike terms, usually joined by addition or subtraction. The expression 3x^7 y^5 only has one term, so it cannot be a binomial.
The degree of a monomial is determined by adding the exponents of all the variables present. In this case, the degree of the monomial is 7 because the exponent of x is 7.
Therefore, the expression is a monomial with a degree of 7, and Sam's statement is correct.