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Adding and Subtracting Polynomials - Problem 2
Even though you guys are going to see problems like this in your Algebra class, sometimes they also involve geometry ideas like perimeter. But you guys already know perimeter means right? Perimeters means the distance around the outside and the way you find it is by adding up all the side.
So I have this funny little shape here and I need to add up all the sides. Write an expression for the perimeter of the given figure. Okay so I’m just going to write a polynomial that represents adding up all of these sides. First thing I’m going to have to add is 3x² plus 8, that’s this side, to that I’m going to add 8x, there’s that side. I’m going to add 3x² more and then finally I’m going to add 5x take away 6. What I did was rewrite each of my sides, but all being added together because perimeter means the sum of the side lengths.
Now it’s just a matter of combining like terms and you guys know how to do that. First I’m going to look for the x² terms, then I’m going to look for the regular Xs, and then the constants. So I have 3x²', plus 3 more x² so that’s 6x². Now I’m going to look for the regular x terms so that will be in standard form, meaning decreasing exponents.
So I did my x² here come to the first, 8x plus 5x is 13xs. Last, but not least I have my constant terms meaning there’s no Xs. 8 take away 6 is +2, that’s it that’s my expression for the perimeter. The perimeter is 6x² plus 13x plus 2 and then in the future you guys you're going to be asked to solve for x in some situation, but for now you’re just working on writing the expression or writing the polynomial.
When you do this just be really careful again make sure every term shows up in your answer. Don’t leave anything out. That’s the most common error people will make is by like forgetting an 8x or forgetting that +8 or some thing. Just be really careful, good attention to detail and you guys can get these problems right.