Problem

How do you recognize like terms?

00:57

Problem 110 Hard Difficulty

Auto Mechanics. The length of a fan belt that wraps around three pulleys is $\left(3 x^{2}+11 x+4.5 \pi\right)$ in. Find a polynomial that represents the unknown length of a part of the belt shown in the illustration below.

Answer

$4 x^{2}+26$

Related Courses

Algebra

Elementary and Intermediate Algebra 5th

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

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Video Transcript

and this problem. We're given the picture of a fan boat, and we're told that it's told the length is three x squared plus 11 x plus 4.5 pot. And what we're trying to do is we're trying to find that missing Lee. So I did the best I could to try and re create that diagram over here on the right. So because we told the total length we know that when we add up each of these sides, it should equal to that length. So that's exactly what we're gonna do. We're gonna add each of those sidelines, including our Blake one, because we know what it should add up to. So we know that X squared minus three x plus 1.5 pie. Excuse me? I put an X there. That should be a pie. Plus Jew pie plus X squared. Plus five X plus five. Plus that unknown side, which I'm gonna call it a question mark, but we know this should all equal to three x squared plus 11 necks. I'm gonna put it right here. Come running out of room plus 4.5. So one thing we can do on the left hand side is we can combine our life terms. So let's start with X squared. X squared also has a like square X squared. Remember, keep in mind that they have coefficients of ones in front of him. Well, one plus one is equal to two, so we'll have to x squared. So now let's move to our next term. Negative three. Ex. Well, it has a late term, a positive five X Well, negative three plus five is equal to two, so we'll have plus two X. Next we have 1.5 pie. Well, it's like terms are two pie as well as pie and keep in mind in front of the pie. There's also imagine everyone. So we have 1.5 pi plus two, which is 3.5 pi plus one is 4.5 pie. So plus 4.5 pie and then we're gonna have plus our unknown, which we're calling the question mark. But again, we know this is equal to three x squared plus 11 x plus 4.5 pie. Well, what if we now subtracted the terms on the left? From there light terms on the right in other words, essentially just kind of solve this equation. So what I mean is we can subtract two x squared from it's like term on the opposite side of the equation. We can also subject to X from its late term on the other side of the equation. And we could subject 4.5 pie from its late term on the other side of the equation. And again, the reason we can do this is because two X squared minus two X squared zero. It will cancel two x minus two x zero that will cancel and 4.5 pi minus 4.5. Pie is zero, so that will also cancel. So now all we're left with is our unknown piece. So now let's simply combine like terms well. Three X squared minus two X squared is equal to one x squared 11 x minus two X is positive Night X and 4.5 pi minus 4.5 pie is zero. Those terms will cancel out. So now what we found is that missing link would be represented by the polynomial X squared plus nine x

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