Terms with Powers

A polynomial is a sum of terms, where each term is a coefficient times a power of $x$. $4x^{2}+x+2x^{2}$ is a polynomial. Its terms are $4x^{2}$, $x$ and $2x^{2}$.

Polynomials are named by their number of terms. A monomial has one term, such as $3x^{2}$. A binomial has two terms, such as $x+5$. A trinomial has three terms, such as $x^{2}+3x+2$. With more than three terms, the name is just polynomial. The prefix poly means many.

You simplify a polynomial by collecting like terms, the same as before. In $4x^{2}+x+2x^{2}$, the terms $4x^{2}$ and $2x^{2}$ are like terms, so they add to $6x^{2}$. The term $x$ has a different power, so it stays on its own. The result is $6x^{2}+x$.