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 + 15

Accepted Answer

Hello, everyone. We're being asked to perform a factorization in the given expression or categorize it as a prime trinomial. Also, we need to perform a check using the foil method. The trinomial we are given is M squared minus M plus 55. Our answer choices are a, the parentheses M plus five multiplied by the parentheses. M plus 11 B, the parentheses, M -1 multiplied by the parentheses. M -55 C, the parentheses, M plus 55 multiplied by the parentheses. M plus one D, the parentheses M -5 multiplied by the parentheses. M -11, rewriting my original trinomial. I have M squared minus 16 M plus 55. I recall that to factor a trinomial. I'm going to end up with two binomials. So this means I am going to open two sets of empty parentheses and fill in the terms I need based on the information in my original trinomial. I know that in my binomial, the first term in each needs to multiply together to the first term in the trinomial. So two things that will multiply to M squared are M and M. So the first term in each binomial is M. Next, I need to find two values that not only multiply to a positive 55 but add to a negative looking at the signs, I know that I need two negatives or I could put both minus signs into my parentheses right now. So I have M and minus sign in both parentheses. This is because I recall that a negative times a negative is a positive, but a negative plus a negative is a negative. So now I could just think about what could multiply to 55 and add to 16. Well, I could check one in 55 that definitely multiplies the 55, but it does not add to 16. The next one that comes to mind would be the pairing 5 and five multiplied by 11 will give me 55 plus 11 will give me 16. So it sounds like five and 11 are good choices for my last terms in my bin no meals. So right now we have the parentheses M - multiplied by the parentheses M -11. This is likely my factorization, but we are going to check it first. So check, recalling that foil means first, outer, inner and last. That's the order we're gonna multiply through. This first would be the first terms in each binomial multiplied together. So M multiplied by M which gives me M squared outer would be M multiplied by negative 11, which would be negative 11 M inner which is negative five multiplied by M. So negative five M last negative five multiplied by 11 or sorry by negative 11, which would give me a positive 55. I'm going to combine my like terms, I have a negative 11 M and a negative five M that can be combined. So I have M squared minus 16 M plus 55 that matches my original trinomial. So I know my factorization is correct. This means our solution is parentheses, M -5 multiplied by the parentheses M -11. And that's answer choice. D 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 + 15

Key Concepts

Factoring Trinomials

Prime Trinomials

FOIL Method

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