Module 7: Algebra

Polynomial refers to any general algebraic expression featuring one or multiple unique terms. The prefix “poly-“ is swapped out when referring to an algebraic expression with a defined number of unique terms.

For example, a monomial features one term, a binomial features two, a trinomial features three, etc.

As a consensus, algebraic expressions are usually written where the higher degree terms are written first. For example, let’s look at the polynomial below:

${"version":"1.1","math":"20x^2+4x+6x-10"}$

Remember:

• 20, 4, 6 are all coefficients.
• 10 is a constant (${"version":"1.1","math":"-10"}$).
• There are currently four terms.
• ${"version":"1.1","math":"4x"}$ and ${"version":"1.1","math":"6x"}$ are like.
• ${"version":"1.1","math":"4x,\;20x^2,\;-10"}$ are unlike.
• ${"version":"1.1","math":"4x"}$ is a lower degree compared to ${"version":"1.1","math":"20x^2"}$.

There are many ways to use and manipulate algebraic expressions. We’ll discuss this more in detail in the next section. For now (and this should usually be your first step), let’s simplify this expression by combining like terms:

${"version":"1.1","math":"20x^2 + 4x + 6x – 10 = 20x^2 + 10x - 10 "}$

To combine terms, pay attention to the sign associated with the terms being combined. In the example above, the like terms are ${"version":"1.1","math":"+4x"}$ and ${"version":"1.1","math":"+6x"}$. Thus, ${"version":"1.1","math":"+4x+6x "}$ was done to combine them.