Expressions Vocabulary

<a href="https://www.prepswift.com/quizzes/quiz/prepswift-expressions-vocabulary" target="_blank">Expressions Vocabulary Exercise</a> Note: about 1:22 into the video, he says something on the lines of "can't include x0". That isn't correct, because the x0 term is the constant term, which can be part of a polynomial. x raised to a negative power won't work however. If you were missing learning vocab in quant, I've got some good news for you. Algebraic expressions contain a bunch of vocab to fulfill that insatiable hunger: Let's look at this expression and dissect it: $4x^2+7x-9$. <ul> <li>Term: Anything that is separated by $+$ or $-$ signs. In this case, $4x^2$, $7x$, and $-9$.</li> <li>Constant: Terms that are not connected to variables, like the $9$ chilling at the end.</li> <li>Coefficient: Any integer connected to a variable within a term. In this case, the $4$ and the $7$.</li> <li>Polynomial: A bunch of terms containing variables, coefficients, and constants.</li> </ul> Polynomials have an important rule we need to follow: Any variables need to have non-negative exponents; a term like $6x^{-4}$ would mess things up. It's like bringing a porcupine to a balloon party. Like Terms share the same set of variables raised to the same exponent. Here's an example: $3y^2 + y^2 - 4y + 2y$ Notice that the first and second terms both have $y^2$ and the third and fourth terms both have $y$. We can "combine" (basically sum up) like terms to make the expression simpler: <ul> <li>$3y^2 + y^2 - 4y + 2y$</li> <li>$(3y^2 + y^2) + (-4y + 2y)$</li> <li>$4y^2 - 2y$</li> </ul> Combining like terms is like tidying up your room—everything in its place and much easier to manage!