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 + 8x + 12

Accepted Answer

Hello, everyone. We've been asked to perform factorization in the given expression or categorize it as a prime trinomial also perform a check using the foil method. The expression we're given is X squared plus 10, X plus 21. Our answer choices are a, the parentheses X plus one times the parentheses, X plus 21. B, the parentheses X plus three multiplied by the parentheses, X plus seven C, the parentheses X -1 multiplied by the parentheses, X -21 D, the parentheses X -3 multiplied by the parentheses X -7, rewriting my original trinomial again, I have X squared plus 10, X plus 21 and I recall that a trinomial will be factoring into two binomials. So I'm gonna open two sets of parentheses next to each other. So I can fill them in as my binomial factorization. First, I know I want to put the first term in each binomial to multiply to the first term in my trinomial. So since the first term in my trinomial is X squared, I want the first term in each binomial to be X next to find the last term in each binomial, I need to find values that will multiply to 21 and add to 10. Since both values are positive, I'm gonna put a plus sign next to each X and then go back to thinking about what can multiply to 21 and possibly add to 10. So 21, I could multiply one times 21 that does not add to 10, three times seven multiplies to 21 and it does add to 10. So I'm gonna put three as the second term in my first binomial and seven is the second term. And my second binomial right now, I have the factorization parentheses X plus three multiplied by the parentheses X plus seven. I think this is done, but I need to check it with the foil method first. So if we call it foil, it means first. So the first terms multiplied together X times X which is X squared outer. So the outer two X times seven. So plus seven, X in 3 times x is 3, X last 3 times 7 is positive 21. When I combine my like terms, I get X squared plus 10, X plus 21 that checks out with my original trinomial. So that means I factored it correctly. So the parentheses X plus three multiplied by the parentheses X plus seven is my answer and it 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 + 8x + 12

Key Concepts

Factoring Trinomials

Prime Trinomials

FOIL Method

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