Identify each expression as a polynomial or not a polynomial. For...

Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. (2/3)t^6+(3/t^5)+1

Accepted Answer

Hello. Today we're going to be determining whether the given expression is a polynomial or not. So what we are given is 5/9 times the quantity eight to the power of four plus eight over a cubed minus 12. So there's a little bit of simplification that we can do to the current expression. And that's gonna be rewriting the eight over a cubed term. C. Eight over a cubed can be rewritten as eight times the quantity one over a cubed. And using our property for negative exponents. We can rewrite this product as eight times the quantity eight to the power of negative three. So if we make the substitution to the current expression, what we have is 5/9 times eight to the power of four plus eight times eight to the negative third power minus 12. Now the rule for this being a polynomial is that every degree or every power in every term must be a positive integer. But here -3 is not a positive integer, it's a negative integer. So since we have a negative integer in the given expression, this automatically means that this is not going to be a polynomial. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to determine whether an expression is a polynomial or not. And I'll go ahead and see you all in the next video

Struggling with College Algebra?

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. (2/3)t^6+(3/t^5)+1

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