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 + 4x + 4

Accepted Answer

Welcome back. I'm 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 polynomial we're given is S squared plus eight S plus 16. Our answer choices are answer choice. A open parentheses. S plus four, close parentheses, squared. Answer choice B open parentheses as plus eight, close parentheses, squared, answer choice, C open parentheses. S plus two, close parentheses multiplied by open parentheses. S plus eight, close parentheses and answer choice D this polynomial is prime. Well, 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 the first term is S squared, not all three terms have an S in them. So there is not anything that we can factor out. Next. We will set up two sets of parentheses and essentially do the reverse of the foil process. We ask ourselves what multiplied by what gives us S squared. Those will be our firsts and the two factors that multiply to equal S squared R S multiplied by S Next, we will ask ourselves what multiplied by what gives us a positive 16. Those will be our last. Well, we have quite a few options for factors that multiply to equal positive 16. But to narrow that down, we know that 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 that to our insides, which is the last from the first set of parentheses multiplied by the first, from the second set of parentheses. Those must add together to equal our middle term from our try no meal, this positive eight s. And so we ask ourselves again what multiplied by what equals positive 16, but also adds up to a positive eight. And those two factors are going to be a positive four. So plus four and another positive four. So our two parentheses read S plus four, multiplied by S plus four. And we know we can rewrite this as open parentheses. S plus four, close parentheses squared. And we look at our answer choices and this matches with answer choice a while 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 + 4x + 4

Key Concepts

Perfect Square Trinomials

Factoring Polynomials

Prime Polynomials

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