What is a polynomial function and its examples?

Aug 09, 2022, 16:45 IST

Polynomial Function

Polynomial is an algebraic expression having one or more terms involving powers of the variable.

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An expression P(x) of the form: P(x) = a_nxⁿ + a_n-1x^n-1 + a_n-2x^n-2 + …….. + a₁x +a₀ where all  a₀  , a₁  , a₂  .......a_n are real numbers and n is non-negative integer (i.e. whole numbers) is called a polynomial.

The Polynomials are also classified on the basis of their degrees 

1. Zero Polynomial Function : A zero polynomial function is of the form f(x) = 0, yes, it simply contains just 0 and no alternative term or variable. Since f(x) = a constant here, it is a constant function.

2. Linear Polynomial Function : A linear polynomial function has a degree 1. It is of the form f(x) = ax + b. Some examples of a linear polynomial function are f(x) = x + 3, f(x) = 25x + 4, and f(y) = 8y – 3.

3. Quadratic Polynomial Function : A quadratic polynomial function has a degree 2. It is of the form f(x) = ax2 + bx + c. Some examples of a quadratic polynomial function are f(m) = 5m2 – 12m + 4, f(x) = 14x2 – 6, and f(x) = x2 + 4x.

4. Cubic Polynomial Function : A cubic polynomial function has a degree 3. It is of the form f(x) = ax³ + bx² + cx + d. Some examples of a cubic polynomial function are f(y) = 4y³, f(y) = 15y³ – y² + 10, and f(a) = 3a + a³.

What is a polynomial function and examples? Pdf