Polynomial function

By definition, a polynomial function is a function that can be written as shown below:

f(x) = a_nxⁿ + a_n-1x^n-1 + ... + a₂x² + a₁x¹ + a₀

You could also use p(x) instead of f(x) in order to be more precise.

p(x) = a_nxⁿ + a_n-1x^n-1 + ... + a₂x² + a₁x¹ + a₀

Notice the following important conditions about a polynomial function

• n is a nonnegative integer or an integer that is either positive or zero

• The coefficients a_n , a_n-1 , ... , a₂ + a₁ , a₀ are real numbers and they are constants

The terms in the polynomial function above are in descending order by degree

For example, the following is a polynomial function.

p(x) = -2x⁵ + 6x⁴ + 10x³ + -3x² + 5x + 9

-2x⁵ is the quintic term

6x⁴ is the quartic term

10x³ is the cubic term

-3x² is the quadratic term

5x is the linear term

9 is the constant term

How to name a polynomial function

p(x) = 6x⁴ + 5x is a quartic binomial

p(x) = -2x⁵ + 6x⁴ + 9 is a quintic trinomial

p(x) = -2x⁵ + 6x⁴ + 10x³ + -3x² + 5x + 9 is a quintic polynomial of 5 terms

p(x) = 5x + 9 is a linear binomial

p(x) = -3x²  is a quadratic monomial

p(x) = -10x³ + -3x² + 5x + 9 is a cubic polynomial of 4 terms