Factor completely, or state that the polynomial is prime. 64-x^2

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Accepted Answer

Hi there. So if this problem says the fact that they've given paul memo completely or categorize the polish prime. If it doesn't get factories furthermore, some We have -4 X Square. So this is a special case for a polynomial and where we can use what's called the difference of two squares zero. So this is the theorem that's in your book. The difference of two squares theorem states that we have a polynomial A squared minus B squared. It factors out to the factors of a plus B times a minus B. Just look at our polynomial. Some we have a squared minus B squared in this case are a squared, it's our 100. R b squared is our four X squared. So Let's say we have a squared equal to 100. Well, if you want to find what A is, we could take the square root the square of a square in the square of 100 squared up. A square just turns out to be a Squared of 100. We know is equal to 10 Sort of a. There is 10. You can do the same for the B. So b Squared is equal to four x squared. Now take the square root of B squared squared B squared. Let me get a B on the left side. Now the square of four X squared. Since this is all multiplying each other, we just take the square root of each of our terms. So the score of four, we know is to the square of X squared. Is this X. So a is 10 RB is two x. So by our difference of two squares, we say we have 100 minus four squared. This is going to be equal to Are a plus B or R 10 plus two X. Multiplied by R 10 -2 x meaning that the factors of this polynomial are just 10 plus two X. 10 minus two X. Our answer is then answer D. Alright, I hope to help you solve the problem. Thank you for watching. Goodbye.

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