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

Welcome back. I am so glad you're here. We are asked to completely factories the following polynomial expression. If possible, otherwise declare if the expression is a prime polynomial, the expression were given is 11 K squared plus 11 D squared. And our answer choices are answer choice A 11 multiplied by open parentheses. K squared plus D squared. Close parentheses. Answer choice B 11 multiplied by open parentheses. Que plus de close parentheses multiplied by open parentheses. Que plus de close parentheses. Answer choice C open parentheses. 11 K plus de close parentheses multiplied by Open Parentheses. K -11 D closed parentheses and answer choice D is that this polynomial is prime. Alright. Well, the first step in factoring is that we take a look at all of our terms and we ask ourselves if there are any common factors that we can factor out and both of these terms have and 11. So we can factor out an 11. Next, we look at the variables. One is K squared ones D squared. Those aren't anything in common. So we can't pull out any variables. Now, we ask ourselves if we factored out in 11, what's left for both of these two terms. So we'll take 11 multiplied by open parentheses. Now we divide each of the two original terms by 11 to see what's left and that will go inside the parentheses. So 11 K squared divided by 11 leaves us with K squared and then 11 D squared divided by 11 leaves us with a positive. So plus D squared and we close parentheses. And the next thing we look at what's inside of our parentheses and we see if there's any further factoring that we can do. And we've got two squares here, the K squared and the D squared, however, they are being added and there is no sum of squares. It's only a difference of squares that we can factor. So actually, we have 11 multiplied by open parentheses. K squared plus D squared, close parentheses. And that's as factored as this one is going to get. We look at our answer choices in this matches with answer choice. A well done. We'll catch you on the next one.

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

Key Concepts

Factoring Polynomials

Sum of Squares

Prime Polynomials

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