Question

Why aren’t the following polynomials? y=x^2 +2^x y^2=(x-2)^2-1 y=1/x^2+1/x+1/2

Answer 1

Answer:

Polynomials can have constants (3, -9), variables (x, y), and exponents ($x^{2}$). One thing you can't have is a variable in the denominator. For example: $\frac{2}{x+3}$

Or fractional exponents.

Step-by-step explanation:

a)   $y=x^{2} +2^{x}$

Is not a polynomial because $2^{x}$ does not have the standard form, where variable is the base. e.g. $x^{2}$

b)   $y^{2}=(x-2)^{2}-1$

Is not a polynomial because $y^{2} =\sqrt{y} =y^{\frac{1}{2} }$ has fractional exponents

c)   $y=\frac{1}{x^{2} } +\frac{1}{x+\frac{1}{2} }$

Is not a polynomial because our variable x is in the denominator