Concept Check Kurt factored 16a²-40a-6a+15 by group...

Question

Concept Check Kurt factored 16a²-40a-6a+15 by grouping and obtained (8a-3)(2a-5). Callie factored the same polynomial and gave an answer of (3-8a)(5-2a). Which answer is correct?

Accepted Answer

Hello. Everyone in this video. We're going to be looking at this practice problem where we want to factor the polynomial? 15 X squared minus 24 X minus 25 X plus 40. And we want to use the grouping method to factor the polynomial. So because we're going to be using the grouping method, I'm going to try to associate terms that have similar components. Well in this case you can see that we have three terms that have the variable X. So I'm just gonna go ahead and group the first two terms together. See how we have four. I'm gonna go ahead and group the first two terms together and the last two terms together. So if I do that, my first grouping is 15 X squared minus X Plus the last two terms Which are negative 25 x plus 40. So now I'm going to go ahead and look at these groupings And from each grouping, I want to try to pull out the greatest common factor. So if I look at 15 X squared minus 24 X. I can pull out a three from 15 and 24. But I can also pull out an X. Because both of these terms have the X. Variable. So I can pull out an X. So I'm gonna go ahead and pull out three X. And if I pull out three X. From 15 X squared, I'm left with five X. If I pull out three X from negative 24 X I'm left with negative eight. And that's my factory ization from my first grouping, I can go ahead and do the same for my second grouping. So if I look at my second grouping, you can see that I can pull out a five and I can't pull out the variable X. Because it's only present in the first term for this case. So in this case because I have a negative as my first term, I'm going to pull out a negative five so that I can get rid of this negative being my first term. So I pull out negative five. I'm left with five x plus eight or minus eight because I pulled out the negative five. So negative five times negative eight is positive 40. So you just want to make sure that the factory ization works out and you can still get the original. But this is our factory Ization from the groupings. And from here you can see that five X - Is a component in both of those groupings. So I'm going to factor it out once again. And when I say factor it out, you want to imagine these terms or all of these terms in this big parentheses and I can factor out from those big parentheses, five x -8. And when I do that, what's left behind is the three x -5. So notice that if I were to multiply five X -8 to these terms, I'd get the equation above once again. So that means that five x minus eight times three x minus five is the final factory ization for this polynomial. And you can see that that aligns with answer choice A. So hopefully this video helped and see you next time.

Concept Check Kurt factored 16a²-40a-6a+15 by grouping and obtained (8a-3)(2a-5). Callie factored the same polynomial and gave an answer of (3-8a)(5-2a). Which answer is correct?

Key Concepts

Factoring by Grouping

Equivalent Expressions and Factoring

Distributive Property and Sign Changes

Watch next

Concept Check Kurt factored 16a2-40a-6a+15 by grouping and obtained (8a-3)(2a-5). Callie factored the same polynomial and gave an answer of (3-8a)(5-2a). Which answer is correct?

Key Concepts

Factoring by Grouping

Equivalent Expressions and Factoring

Distributive Property and Sign Changes

Watch next

Concept Check Kurt factored 16a²-40a-6a+15 by grouping and obtained (8a-3)(2a-5). Callie factored the same polynomial and gave an answer of (3-8a)(5-2a). Which answer is correct?