Factor out the greatest common factor from each polynomial. See E...

Question

Factor out the greatest common factor from each polynomial. See Example 1. 2(m-1)-3(m-1)^2+2(m-1)^3

Accepted Answer

Hello. Everyone in this video. We're gonna be looking at this practice problem where we want to factor the expression seven times B plus two to the third Power minus three times B plus two to the second power plus 11 times B plus two. So in this case because we're going to be factoring, we want to try to look for a common factor amongst all of these terms. So if we look at all the factors you can see that they all have a B plus two component. This first term has B plus two to the third. The second term has B plus two squared and the last term has B plus two to the first power. So because that last term has B plus two to the first power. That means that the common factor is B plus two to the first power. Because if I had B plus two to the second power you can see that this last term doesn't have a B plus two to the second power. So I'm just gonna say B plus two to the first power. So if I take out B plus two to the first power from each of these terms, I have seven times B plus two Squared. Now instead of to the 3rd minus three times B plus two to the first power. And my last term is now just 11. So each of the B plus two lost power. Because when you think of taking out the common factor, remember that it's still there. It's just on the outside. So if I were to multiply it back in or get rid of the factory ization it would go back to my original expression. So now that I took out the common factor, I'm going to focus on simplifying this part of the expression. So in order to simplify this expression, I need to get rid of this exponent here where I have B plus to squirt And I also need to distribute the seven and the -3. So I'm gonna go ahead and start doing that. So I have seven. And if I expand the exponents B plus two squared, I have B plus two times B plus two minus negative three times B is negative three B negative three times positive two is negative six. And I still have this positive 11. And from here you can see I can combine negative six and positive 11. Leaving me with five positive five, I still have the negative three B. And now I can use the foil method to multiply B plus two times B plus two. So I have B times B is B squared. The first terms. Then the outer terms b times two is to be. And then the inner terms two times B is again to be. And finally the last terms Just two times or positive four. And remember that this is still being multiplied by this seven. So from here you can see that I can combine these middle terms. So two B plus two, B is equal to four B. And now I can go ahead and distribute this seven. So seven times B squared is seven B squared seven times four B is 28 B. and seven times 4 is 28. I still have -3b plus five. And again I want to combine the like terms. So I have this 28 and this five, so 28-plus 5 is 33. And then I have this 28 b. and -3 b. So 28 B -3 b. is 25 b. And then the seven B squared has no like term to combine with. So I just write seven b squared. So now we've fully distributed the seven and the three and expanded the exponents and the expression. And you can see that there's nothing else that we can really simplify so we can bring back the common factor. So our factory Ization for the expression is B plus to the common factor times seven B squared Plus 25 B plus 33. So this becomes our final factory Ization for the expression. And you can see that that aligns with answer choice A. So hopefully this video helped and see you next time

Factor out the greatest common factor from each polynomial. See Example 1. 2(m-1)-3(m-1)^2+2(m-1)^3

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

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