In Exercises 65–92, factor completely, or state that the polynomi...

Question

In Exercises 65–92, factor completely, or state that the polynomial is prime. 9x^3−9x

Accepted Answer

Hello today we're going to be factoring a given polynomial. The polynomial given to us is three X cubed minus 48 X. Now looking at both of the terms given each term has a factor of X and both terms are divisible by three. So we can go ahead and factor out a three X from our given polynomial. Factoring out of three. X is going to give us three X times the quantity X squared minus 16. All right. Now, if we look at the given polynomial, X squared is a perfect square because X squared is x times X and 16 is a perfect square because 16 is four times four. So we can factor this binomial using the difference of squares, difference of squares and what that states is if we have a mano me away in the form of a a squared minus B squared, that is going to equal to a plus B times a minus B. Well, x squared again is X times X. Which we can rewrite as X squared and is four times four. And we can rewrite that as four squared. So we're gonna let our a equal to X and r B equal to four. And rewriting it in this form is going to give us a plus B or x plus four times a minus B or x minus four. And keep in mind that we still have that factor of three X. That we factor out in the beginning. So both these quantities are getting multiplied by three X. And this is going to be the complete factory ization of our given polynomial. That also means that the answer to this problem is going to be D. So I hope this video helps you in understanding how to factor this mono real, and I'll go ahead and see you all in the next video.

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