Intro to Polynomials

Ever wondered why they're called "polynomials"? The word breaks down into "poly" (meaning many) and "nominal" (meaning terms). Polynomials can look like $10x^5 - 9x^2 + 13x + 7$ or be as simple as $7y^9$ or even just a number like 5. Remember though - no negative powers allowed in polynomials!

Polynomials contain different parts worth identifying. Each polynomial consists of terms (like $10x^5$ or $-9x^2$), and every term has a coefficient (the number part), a variable, and a non-negative integer power. When written in standard form, the first coefficient is called the leading coefficient, while terms without variables are called constant terms.

We name polynomials based on how many terms they have. A monomial has just one term, a binomial has two terms, and a trinomial has three terms. The degree of a polynomial is determined by the highest power in any term - so $10x^5 - 9x^2 + 13x + 7$ would be a fifth-degree polynomial.

Quick Tip! When writing polynomials in standard form, always arrange terms from highest power to lowest power. For example, $10x^5 - 9x^2 + 13x + 7$ is in standard form, but $13x + 7 + 10x^5 - 9x^2$ is not!