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

Question

Factor out the greatest common factor from each polynomial. See Example 1. 5(a+3)^3-2(a+3)+(a+3)^2

Accepted Answer

Hello everyone in this studio, we're going to be looking at this practice problem where we want to factor the expression nine times k minus four minus three times k minus four squared plus 13 times k minus four to the third. So in this case because we want to try to factor this expression, we want to try to find the common factor or a common factor that we can get rid of in or bring out from all of these terms. So if we look at nine times k minus four and three times k minus four squared and 13 times k minus four to the third, you can see that k minus four is present in all of the terms. And if we look K - has the least appearances in this nine component because it's k minus four to the first power, which means that we can only take out a k minus four to the first power from all of the components of the expression. So if I take out K -4 from all of these components, I'm left with nine for my first term and then three times k minus four notice how it's no longer squared, but to the first power and 13 times k minus four squared Now instead of two the third And again those came those last two K -4 lost an exponent power. Because what I'm doing when I take out the common factor is I'm bringing it off to the side so that when this becomes multiplied, it gets re applied to all of those terms. But for now because I've already taken out k minus four, I'm going to focus on factoring this section of the expression. So if we look at this expression in order to sort of after this, I need to expand this exponent here where I have K minus four squared, So I can then distribute this 13. But if I look at this three, I can actually go ahead and distribute that already. So it would become 9 -3 times K is three K and negative three times negative four is positive Plus 13. And then I need to expand that exponent. So I would have K -4 Times K -4. So I just expanded this explanation. So now I can do the foil method with these two. So of K times K is k squared oil stands for first terms. Then the outer terms K times negative four is negative four K. And now the inner terms negative four times k is again negative four K. And the last terms negative four times negative four is positive 16. So now I've expanded those, the exponent for k minus four squared. I can combine these middle terms. So I have K squared minus eight K plus 16 And remember that is still being multiplied by 13. So if I take a look at this first part, you can see that I can also combine this nine and this 12. So nine plus 12 is 21. So I have 21 minus three K plus 13 times K squared minus eight K plus 16. So I'm gonna go ahead and multiply that 13 to all those components. So I have 13 times K squared is 13 K squared. 13 times negative eight K Is -104 K. And finally I have 13 times 16. And that is to oh wait So I have plus 208. And once again you can see that we have like terms that we can combine. We have these 21 and the 208 and we also have the negative three K. And negative 104 K. And there's nothing to combine the 13 K squared with. So I'm just gonna say 13 k squared minus negative three k minus 104 K is -107 K. And 21 plus 208 is positive. 200 29. And from here you can see that we can't really factor much out from this expression so are fully factored term For the original expression we have to bring back the common factor K -4. So it'd be K -4 times K squared -107 K Plus 229. So this becomes our final answer for this factory ization. And you can see that this aligns with answer choice B. So hopefully this video helped and see you next time

Factor out the greatest common factor from each polynomial. See Example 1. 5(a+3)^3-2(a+3)+(a+3)^2

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

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