Please help! Is the expression f(x)=18-21x+2^x considered a polynomial? If it is a polynomial, name it according to its degree and number of terms.

Question

directrix · Answer

f(x)=18-21x+2^x considered a polynomial?

Did you mean to write the 2^x in this way?

Or, did you intend to write it as x^2?  @gintoki

anonymous · Answer

Yes 2^x is intentionally written that way in the problem. I believe that the degree of x can be any number so I am unsure if it is a polynomial or not.

directrix · Answer

Check out the two attachments.

anonymous · Answer

Thank you for those. I understand that 6x^-2 cannot be a polynomial, but I cannot find examples that show that the the term 2^x is considered okay

directrix · Answer

2^x is not a term of any polynomial.

anonymous · Answer

I see. Thank you very much for the help.

anonymous · Answer

I'm sorry, could you help me with classifying one more term?

directrix · Answer

A Polynomial can be expressed in terms that only have positive integer exponents and the operations of addition, subtraction, and multiplication. In other words, it must be possible to write the expression without division. It's easiest to understand what makes something a polynomial equation by looking at examples and non examples as shown below. http://www.mathwarehouse.com/algebra/polynomial/polynomial-equation.php

anonymous · Answer

Is $$f(x)=x^2\sqrt{3}+x-5$$ considered a polynomial

anonymous · Answer

So only whole numbers and no radicals?

directrix · Answer

I think you have exponents of the terms of a polynomial confused with the coefficients of the terms of the polynomial.

directrix · Answer

>So only whole numbers and no radicals?

That applies to the exponents of the variable.

directrix · Answer

A coefficient can be a radical.

anonymous · Answer

I am. I was confused at first since I didn't understand where the variable could be and could not be. Thank you. I understand now.

directrix · Answer

Here's something more to read if you are interested. It might help to cement the polynomial concept. It is easy to get mixed up. Just now, I read that a polynomial is of finite number of terms. I'll have to think about that. http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-polynomial-2009-1.pdf

anonymous · Answer

Very helpful and in-depth source. Thank you!