A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants.
A polynomial function in standard form is:
[tex]f(x) = a_n x^n+ a_{n-1} x^{n-1}+ ... + a_2x^2+ a_1 x + a_0.[/tex]
This algebraic expression is called a polynomial in variable x.
Here,
- [tex]a_n, a_{n-1}, \dots a_0[/tex] are real number constants
- [tex]a_n[/tex] can’t be equal to zero and is called the leading coefficient
- n is a non-negative integer
- Each exponent of variable in polynomial function should be a whole number
From the problem,
a) [tex]3x^2-5x^2+7[/tex]
b) [tex]x^2+4x-2[/tex]
e) [tex]x[/tex]
g) [tex]\frac{x^2}{3} +x-5[/tex]
h) [tex]7[/tex]
All five expressions above are polynomial since all of the variables have positive integer exponents.
But expressions like;
c) [tex]2x^{-4}+x^3[/tex]
d) [tex]6x^{\frac{1}{3}}-x^2-1[/tex]
f) [tex]x^3+x^{\sqrt{2}}+1[/tex]
are not polynomials, we cannot consider negative integer exponents or fraction exponent or division here.
So, functions that are not polynomial are C, D, and F.
Learn more about quadratic is here:
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