Find the sum of 5 x 2 − 2 x + 6 5x^2-2x+6 and − 4 x 2 + 2 x + 8 -4x^2+2x+8 .

So, let's take a look at our next practice problem. So, just as a reminder, sometimes in your textbooks, your homework assignments, you may not just already see the two polynomials written out with their symbols and things like that. You may see something like a sentence like find the sum of these two polynomials. So, let's dive into our practice problem. We're going to be finding the sum of five x squared minus two x plus six, and the second polynomial is negative four x squared plus two x plus eight. Now, we could set this up, we could write this out so that if we have the symbols and parentheses and we can combine like terms sort of side by side, but I just want to show you that there is another way to organize this that could be a little bit simpler. We're going to stack these equations vertically, and the basic idea is I want to stack like terms on top of each other. What do I mean by this? Well, I have five x squared minus two x plus six. Now, I'm going to write the symbol here on the left side and we're going to be finding the sum of the two polynomials. So, the sum means I want to write a plus sign here, but But now what I want to do is underneath the five x squared, I want to find the corresponding like term in the second polynomial and write that underneath and then so on and so forth. Now, here I have a negative four x squared. I want to keep the negative sign because there was a negative sign in the second polynomial here. So, what about the x term? I have a minus 2x in the first polynomial and in the second, I have a plus 2x. So, I'm going to write that there. And then finally, the constants, I have a plus six in the first and a plus eight in the second. So, I'm going to stack those two vertically as well. Alright, Once we do this, we just draw a big line and then just do the addition vertically. So, what is five x squared plus negative four x squared? It's basically like you're just doing subtraction. Well, five minus four just becomes a single, x squared. And so, what about the negative two x and the positive two x? Well, actually, what happens here is this just cancels out to sort of zero over here. So, you could either just write nothing, you could write zero x, or you can basically just sort of leave that sort of blank because you've actually skipped this term they've canceled out. And then what about the six and the eights? Well, those things will combine and add to 14, and so really this is all that's left, and now we've done the addition. You can go ahead and just sort of trust and sort of verify, by trying this on your own that if you were to sort of add these two polynomials again side by side like we've done in other practice problems, you would end up with the exact same answer. Alright. So, this is going to be your final answer over here. It's just going to be x squared plus 14. Now, again, just sort of as one thing to watch out for is that sometimes you may not have a bunch of terms that will stack vertically, so you may be having to leave gaps in some of the, the way that you write these things so you can accommodate other terms. Alright? So, XSquaredPlus14 is your answer. Let me let me know if you have any questions, and let's take a look at the next

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Multiple Choice

Find the sum of $5 x^{2} - 2 x + 6$ and $- 4 x^{2} + 2 x + 8$ .

$x^{2} - 6 x + 16$

$x^{2} - 6 x + 14$

$x^{2} + 4 x + 14$

$x squared plus 14$

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Verified step by step guidance

Identify the two polynomials to be added: \$5x^2 - 2x + 6$ and $-4x^2 + 2x + 8$.

Group like terms together. The like terms are the $x^2$ terms, the $x$ terms, and the constant terms:

\[(5x^2) + (-4x^2), \quad (-2x) + (2x), \quad (6) + (8).\]

Add the coefficients of the like terms separately:

\[5x^2 + (-4x^2) = (5 - 4)x^2,\]

\[-2x + 2x = (-2 + 2)x,\]

\[6 + 8 = 6 + 8.\]

Write the resulting polynomial by combining the sums of each group of like terms.

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Find the sum of $5 x^{2} - 2 x + 6$ and $- 4 x^{2} + 2 x + 8$ .