In Exercises 1–30, factor each trinomial, or state that the trino...

Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication.

x² + 9x + 20

Accepted Answer

Hello, everyone. We're going to perform a factorization in the given expression or categorize it as a prime trinomial. Also, we will perform a check using the foil method. The expression we're given is U squared plus 15, U plus 44. Our answer choices are a, the parentheses, U plus one multiplied by the parentheses. U plus 44. B, the parentheses, U plus 44 multiplied by the parentheses. U minus one C, the parentheses, U plus four multiplied by the parentheses. U plus 11 DU - multiplied by the parentheses. U -11, rewriting my original expression. We have U squared plus 15, U plus 44. I recall that when I factor a trinomial, I'm gonna factor it into two binomials. So I'm gonna start two sets of parentheses and currently they're empty, but I'm gonna fill them. The first term in each set of parentheses will be values that will multiply to the first term in my trinomial. So since my trinomial first term is U squared, what makes sense to put there? Is you? So the first term in both sets of parentheses is you because U times you will give me U squared. Next, I need to find two values that not only multiply to positive 44 but will add to a positive since both are gonna be positive. I know that in my parentheses, I will have two plus signs. So both parentheses now stand at U plus. So now to find the values I'm gonna think about what do I know will multiply to 44. I can even make a list off to the side if that helps. I know one and 44 will multiply to 44, but that will not add to 15. So that's not the answer 2 and 22 would multiply to 44, but that will not add to 15. So that's not it four and will multiply to 44. When I add them, they do add to 15. So those are the values that I want to use. So I'm gonna put those in my parentheses. So I will have parentheses U plus four multiplied by the parentheses U plus 11. Now, this is probably my factorization, but I want to check it using the foil method first. Prior to choosing my answer. Recall that foil stands for first, outer, inner and last. And it's the order we're going to multiply this in. So checking it check first would be U times U. So U squared outer would be U times 11. So that'd be 11 U and it's a positive. So we're gonna write it as plus in, it's gonna be positive four multiplied by positive U which would be plus four U and then last will be the last term in each parentheses. So four multiplied by 11, which is 44. When I combine like terms I have U squared plus 15 U plus 44 that does match my original trinomial. So that means our factorization is correct. So the parentheses, U plus four multiplied by the parentheses, U plus 11 is our solution. And answer choice. C have a nice day.

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² + 9x + 20

Key Concepts

Factoring Trinomials

Prime Trinomials

FOIL Method

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