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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To determine the degree of a monomial or a polynomial, we need to analyze the variables and their exponents in the expression.
In the expression 3x7y5, we have two variables: x and y.
Jessica states that the expression is a binomial with a degree of 12. However, a binomial is an algebraic expression with exactly two unlike terms. The expression 3x7y5 has only one term, as there is no addition or subtraction involved. Therefore, Jessica is incorrect.
Sam states that the expression is a monomial with a degree of 7. The degree of a monomial is the sum of the exponents of its variables. In this case, the exponent of x is 7 and the exponent of y is 5. Thus, the degree of the monomial is 7 + 5 = 12. Therefore, Sam is incorrect as well.
In conclusion, neither student is correct. The expression 3x7y5 is a monomial with a degree of 12.