Factor each polynomial by grouping. See Example 2. 10ab-6b+35a-21

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Hello, everyone in this video, we're going to be looking at this practice problem where we want to factor the polynomial to a B minus nine, B minus six A plus 27 we want to factor it using the grouping method. So because we're going to be grouping this polynomial, I want to try to group together terms that have similar variables associated with them. So if you look at the first two terms to A B and negative B, you can see that they're the only terms that have the B variable associated with them. So I'm going to go ahead and group those two terms together. So I'll have to a B -9 B Plus the last two terms, which is -6 a. plus 27. And from here I'm going to look at my two groupings and I'm going to try to factor out the greatest common factor among them. So if I look at two, a B minus nine B. I can factor out the variable B because it's present in both terms. And that seems to be the only factor I can get rid of. So they take out be from to a bi. I'm left with two A. And if I take out be from nine negative nine B. I'm left with negative nine. So I took out the greatest common factor for my first grouping which was B. I can do the same for my second grouping. So if I look at my second grouping I can pull out a a negative three or a positive three. But I'm going to go ahead and pull out a negative three just to get rid of that negative in my first term. So if I pull out negative three, I'm left with positive to A for my first term And -9 for my second term. And I can't really pull out anything else from two a -9. But if we look at our two factors now, you can see that I have two a -9 in both of these factories. Ations. Which means that I can pull out to a -9 once again. And by pull out to a -9, you can assume that there's these parentheses that go over both of these terms. And if I pull out to a -9, I'm left with B -3. And you can see that I can redistribute the two a -9 and I'd go back to the above equation, But to a -9 times B -3 becomes the final factory ization for the polynomial. And you can see that that aligns with answer choice. See so hopefully this video helped and see you next time

Struggling with College Algebra?

Factor each polynomial by grouping. See Example 2. 10ab-6b+35a-21

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