Two students are analyzing the expression 3x7y5
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.
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Neither student is correct.
A monomial is an expression with only one term, while a binomial is an expression with two terms. The expression 3x7y5 has three terms, so it is not a monomial or a binomial.
The degree of a term in an expression is the sum of the exponents of the variables in that term. In the expression 3x7y5, the highest sum of exponents is 7 + 5 = 12. However, we must remember that in an expression, the degree refers to the term with the highest degree, not the sum of the exponents. Since 7 + 5 = 12 is not the degree of the entire expression, Jessica is incorrect.
Sam states that the expression is a monomial with a degree of 7. Since the expression has three terms and a monomial cannot have more than one term, Sam is incorrect.
Therefore, neither student is correct.