<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-expressions-vocabulary" target="_blank">Expressions Vocabulary Exercise</a></span></p>
<p><span style="font-size:18px;"><strong>Note</strong>: about 1:22 into the video, he says something on the lines of "can't include x<sup>0</sup>". That isn't correct, because the x<sup>0</sup> term is the constant term, which <em>can</em> be part of a polynomial. x raised to a negative power won't work however. </span></p><p>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:</p>
<p>Let's look at this expression and dissect it: $4x^2+7x-9$.</p>
<ul>
<li><strong>Term:</strong> Anything that is separated by $+$ or $-$ signs. In this case, $4x^2$, $7x$, and $-9$.</li>
<li><strong>Constant:</strong> Terms that are not connected to variables, like the $9$ chilling at the end.</li>
<li><strong>Coefficient:</strong> Any integer connected to a variable within a term. In this case, the $4$ and the $7$.</li>
<li><strong>Polynomial:</strong> A bunch of terms containing variables, coefficients, and constants.</li>
</ul>
<p><strong>Polynomials </strong>have an important rule we need to follow:</p>
<p>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.</p>
<p><strong>Like Terms</strong> share the same set of variables raised to the same exponent. Here's an example:</p>
<p>$3y^2 + y^2 - 4y + 2y$</p>
<p>Notice that the first and second terms both have $y^2$ and the third and fourth terms both have $y$.</p>
<p>We can "combine" (basically sum up) like terms to make the expression simpler:</p>
<ul>
<li>$3y^2 + y^2 - 4y + 2y$</li>
<li>$(3y^2 + y^2) + (-4y + 2y)$</li>
<li>$4y^2 - 2y$</li>
</ul>
<p>Combining like terms is like tidying up your room—everything in its place and much easier to manage!</p>