Please explain:
Which of the following are polynomials in x?
A: x + 1/x
B: x^3 + 3x^2 + 5x - 2
c: x^4 - 2x^3 + x
D: x^2 + rootx
E: 3 + x
F: 3^x + 2^x

Question

Please explain:
Which of the following are polynomials in x? 
A: x + 1/x
B: x^3 + 3x^2 + 5x - 2
c: x^4 - 2x^3 + x
D: x^2 + rootx
E: 3 + x
F: 3^x + 2^x

anonymous · Answer

the answer in the back says the answer is B, C and E

hero · Answer

See definition of a polynomial here: http://www.mathsisfun.com/definitions/polynomial.html

anonymous · Answer

i'm not sure for f acc. to me all xcept a and d

hero · Answer

A polynomial can have
1. whole number exponents
2. terms connected by addition and subtraction
3. variables and constants

A polynomial cannot have: 
1. negative exponents
2. fractional exponents
3. terms connected by division

anonymous · Answer

hmmm so why is it that 3^x + 2^x cannot be a polynomial?

hero · Answer

Because x is not a whole number exponent. It is considered an infinite variable that can be represented by any real number. That would include things such as fractions, irrational numbers, negative exponents etc.

anonymous · Answer

ohh okay i think i get it now, thankyou!

anonymous · Answer

yep thanks :)

hero · Answer

I'll add another line to the previous statement:

A polynomial can have
1. whole number exponents
2. terms connected by addition and subtraction
3. variables and constants

A polynomial cannot have: 
1. negative exponents
2. fractional exponents
3. terms connected by division
4. Infinite variable exponents

hero · Answer

Okay that should be good enough