Understanding Polynomials
Ever wondered what makes a mathematical expression a polynomial? A polynomial is a function expressed as a sum of terms with variables raised to whole number powers. Not everything qualifies though - expressions with negative exponents, variables in denominators, or radicals containing variables are not polynomials.
The general form of a polynomial function looks like:
f(x) = anx^n + an-1x^n-1 + ... + a1x + a0
where n is the degree (highest exponent) and the a-values are coefficients.
Polynomials come in different forms based on their number of terms:
- Monomials have just one term (like 5x or 7)
- Binomials contain two terms (such as 2x+7)
- Trinomials have three terms
Quick Tip: You can quickly identify polynomial types by counting their terms, and their degree by finding the highest exponent on any variable.
The degree also tells us what type of function we're dealing with. Linear functions (degree 1) create straight lines, while quadratic functions (degree 2) form parabolas when graphed.
