Question

Identify ALL expressions that could be defined as a polynomial:

1. 2x^2-15x+10
2. (5x^2y^3)/(z)
3. (2m^4-r^3)/(5)
4. 9x^-3+8
5. 8x-2^-2

Answer 1

Hint: any time you are dividing by a variable or have a negative exponent for a variable, then it is NOT a polynomial

Answer 2

ex:

2/x is NOT a polynomial

x^(-3) is NOT a polynomial

Answer 3

So if there is a negative exponent it is automatically NOT a polynomial?

Answer 4

well if you had 2^(-2), then no it could be a polynomial because it needs to be over a variable

Answer 5

ex: x^(-2) is NOT a polynomial

but...

x^2 + 2^(-2) is a polynomial

Answer 6

so assuming #5 has no typos, 8x-2^-2 is a polynomial

Answer 7

but....4. 9x^-3+8 is NOT a polynomial

Answer 8

And please correct me if I am wrong, but 1 and 2 are polynomials?

Answer 9

1 is, 2 is not

Answer 10

notice how you're dividing by z (a variable)

Answer 11

in #3, you aren't dividing by a variable (it's just a constant 5), so it's a polynomial (you don't have negative exponents either)

Answer 12

I think I get it..

Answer 13

other things that make an expression not a polynomial

1) if you have a square root over a variable

2) if you have some trig function applied to a variable (eg: sin(x))

3) if you have a log applied to a variable (ex: log(x) )

there are many more criteria, but for now just knowing if you have a variable in the denominator or a negative exponent over a variable, it won't be a polynomial

Answer 14

ok just keep practicing it

Answer 15

Thank you sooooo much :D

Answer 16

you're welcome