In Exercises 23–48, factor completely, or state that the polynomi...

Question

In Exercises 23–48, factor completely, or state that the polynomial is prime.8x² - 8y²

Accepted Answer

Hello, everyone. We've been asked to completely factorize the following polynomial expression. If possible. Otherwise declare if the expression is a prime polynomial, the expression we're given is 27 U squared minus 27 T squared. Our answer choices are a, this polynomial is prime B negative three, multiplied by the parentheses. Three, U minus T multiplied by the parentheses. Three, U plus T C negative multiplied by the parentheses. U minus T multiplied by the parentheses, U plus T D negative multiplied by the parentheses T minus U multiplied by the parentheses T plus U rewriting our original polynomial. We have 27 U squared minus 27 T squared. I recall that when I factor, I want to find a G C F if there is one. So finding the greatest common factor or the largest value that will come evenly out of both terms. In this case, I noticed that both terms have a coefficient of 27. I'm gonna factor 27 out of my original polynomial. And actually I'm gonna factor out negative 27 because this will make it. So I now have negative 27 multiplied by parentheses negative U squared plus T squared. And I'm gonna rewrite that one more time flipping the location of the U squared and the T squared. So my current factorization is negative 27 T squared minus U squared. I did this just to have my answers in alphabetical order. Excuse me, I mean, my variables in alphabetical order just because oftentimes that's what our answer choices have them set up as So -27 stays on the outside. And then I noticed that in my parentheses, I have the difference of two squares. I recall to factor the difference of two squares. I'm gonna open two sets of parentheses, they're currently empty, but I'm gonna fill them using a certain factorization. So when I'm working with the difference of two squares, the first term in each new binomial is the square root of the first term of the difference of two squares. So the square root of T squared is T and that's the first term in each parentheses that I just made. The last term in our new binomial is the square root of the last term from the difference of two squares. So the square root of U squared is U. And I recall that the signs between my two terms, one will be a minus sign, one will be a plus sign. So my factorization is negative 27 multiplied by the parentheses T minus U multiplied by the parentheses T plus U. That is our final factorization, there's nothing further to factor and that's answer choice. D have a nice day.

In Exercises 23–48, factor completely, or state that the polynomial is prime.8x² - 8y²

Key Concepts

Factoring Polynomials

Difference of Squares

Greatest Common Factor (GCF)

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