Factor each polynomial by grouping. See Example 2.

Question

20 z^{2} - 8 x + 5 p z^{2} - 2 p x

Accepted Answer

Hello, everyone in this video, we're gonna be looking at this practice problem where we want to use grouping to factor the polynomial 63 A squared minus 27 B plus seven A squared times C minus three BC. So in this case, we're going to be factoring by grouping, which means that we want to try to pair terms that have like terms together. And in each of those groupings, we want to make sure that there's at least two terms. So you can see that we're working with 1234 terms. So we want to break them into two groupings so that there's two terms in each of those groupings. And if we look at the problem, you can see that the last two terms have ac variable in them. So those would be best grouped together. And these first two terms would then be grouped together even if they don't have the same variables. So my two groups would be 63 A squared minus 27 B plus my second group, which is seven A squared times C minus three BC. And from here, I'm gonna go ahead and try to pull out like terms from these equations. And by like terms, I also mean common factors or the greatest common factor. So if we look at this first section 63 A squared minus 27 B, you can see that I can pull out a nine. And if I pull out a nine from 63 A squared, it becomes seven A squared. If I pull out A nine from 27 becomes three. And I solved that B So my first term is now nine times seven A squared minus three B and I still have this second portion here. And if I look at the second term, seven A squared times C minus three BC, you can see that I can pull out ac from both of these terms. So if I pull out the C, I'm left with C times seven A squared minus three B, well, if we look at our equation, now, you can see that I have seven A squared minus three B left in both of these terms, which means that I can actually factor seven A square to minus three B out. So if I do that seven A squared minus three B, I'm left with this nine plus the sea and notice how these equations are the exact same. It's just if I did multiplication and distribute it again, I'd go back and now we have our final factorization for the polynomial. So this becomes our final answer. Seven A squared minus three B times nine plus C and you can see that, that aligns with answer choice B. So hopefully this video helped and see you next time.

Factor each polynomial by grouping. See Example 2. $20 z^{2} - 8 x + 5 p z^{2} - 2 p x$

Key Concepts

Polynomial Grouping

Greatest Common Factor (GCF)

Factoring Polynomials

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