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 + x − 30

Accepted Answer

Hello, everyone. We've been asked to perform a factorization in the given expression or categorize it as a prime trinomial. Also, we are going to perform a check using the foil method. The expression we're given is T squared plus two T minus 143. Our answer choices are a, the parentheses T plus 11 multiplied by the parentheses. T plus 13. B, the parentheses T minus 11 multiplied by the parentheses T plus C, the parentheses T plus 11 multiplied by the parentheses. T minus 13 D, the parentheses T -11 multiplied by the parentheses. T -13. Going back to my original expression, I have T squared plus two T -143. I recall that when I want to factor a trinomial, I'm gonna try to factor it into two bin, no meals. So I'm gonna open two sets of parentheses next to each other. They are currently empty, but we will fill them with information from the trinomial. First looking for the first term in each binomial. I need to pick values that will multiply to the first term in the trinomial. So the first terminal trinomial is T squared So to get T squared, the first term in each binomial will be the value T. Next, I need to find two values that not only multiply to negative 143 but will add to a positive two T because it multiplies to a negative number. I know that the signs in my binomial will be one plus sign and one minus sign. So I'm gonna put those in right now. So in my parentheses, I have a T minus and then an empty space and my next set of parentheses has a T plus sign and then an empty space. So I need to come up with numbers that will multiply to 143 and then check to see if it will add to a positive two. I know negative one and a positive 143 would multiply, but that definitely doesn't add to two. Um Same with a positive one and a -143. There's no way that's gonna add to a positive too. The only other pair of factors I can come up with that will multiply it to 143 are 11 and 13. Since I know one needs to be positive and one needs to be negative, I'm gonna try negative 11 and positive 13 that does multiply to negative 143 and it will add to a positive too. So this is my combination. So the 11 goes with the minus sign and the 13 goes with the plus sign. So at this step, I have the factorization parentheses T minus 11 multiplied by the parentheses T plus 13. We need to check it using the foil method. Recall that foil stands for first, outer, inner and last. So it's the order we're going to multiply these values in first is T times T which will result in T squared outer T multiplied by 13. So plus 13 T in negative 11, multiplied by T results in negative 11 T and last negative 11 multiplied by 13 will be -143. So at this step, I have T squared plus 13 T minus 11 T minus 143 I wanna combine my like terms which are my T terms. And when I do that, I get T squared plus two T minus 143 that matches my original trinomial. So our factorization checks and our solution is the parentheses T minus 11 multiplied by the parentheses T plus 13, which is answer choice B 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 + x − 30

Key Concepts

Factoring Trinomials

Prime Trinomials

FOIL Method

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