In Exercises 49–64, factor any perfect square trinomials, or stat...

Question

In Exercises 49–64, factor any perfect square trinomials, or state that the polynomial is prime.

x² − 10x + 25

Accepted Answer

Welcome back. I am so glad you're here. We are asked to completely factories the following perfect square, try no meal. If possible. Otherwise declare if the expression is a prime polynomial, the expression were given is S squared minus eight S plus 16. Our answer choices are answer choice. A open parentheses, S minus two, close parentheses, squared. Answer choice B open parentheses, S minus four, close parentheses squared, answer choice C open parentheses, S minus eight, close parentheses squared, an answer choice D this polynomial is prime. The first step in factoring is that we look at all of our terms and ask ourselves if there are any common factors that we can factor out. And this first term has an S squared but not all three terms have an S so we can't factor anything out. And next, we're going to set up two sets of parentheses. We're essentially going to do the reverse of the foil process. We start off by asking ourselves what multiplied by what equals S squared. Those are going to be our firsts. And the two factors that multiply to give us X squared are going to be S multiplied by S And now that we have our first established, we ask ourselves what multiplied by what gives us a positive 16. Those are going to be our lasts. There are quite a few factors that multiply to equal positive 16. But we have another clue here. Not only does it multiplied, equal positive 16, they also need to when we take our outsides, which is the first from the first set of parentheses, multiplied by the last from the second set of parentheses and add those to our insides, which is the last, from the first set of parentheses multiplied by the first from the second set of parentheses. Those need to add up to equal this middle term from our try no meal, this negative eight S and so what multiplied by what gives us a positive 16 but adds up to a negative eight, that's going to be a negative four multiplied by a negative four and a negative four added to a negative four. So each set of parentheses will have a minus four in it. So they read S minus four multiplied by S minus four. And we know that we can rewrite that as open parentheses. S minus four, close parentheses squared. And now we look at our answer choices and that matches with answer choice. B well done. We'll catch you on the next one.

In Exercises 49–64, factor any perfect square trinomials, or state that the polynomial is prime. x² − 10x + 25

Key Concepts

Perfect Square Trinomials

Factoring Polynomials

Prime Polynomials

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