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.y² + 10y + 16

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'll be performing a check using the foil method. The trinomial we were given is S squared plus 18 S plus 77. Our answer choices are a, the parentheses S plus seven multiplied by the parentheses. S plus 11 B, the parentheses, S plus one multiplied by the parentheses. S plus 77 C, the parentheses S -1 multiplied by the parentheses. S -77 D, the parentheses S -7 multiplied by the parentheses. S -11. Going back to my original expression, I have S squared plus 18 S plus 77. And I recall that to factor a trinomial, I'm gonna break this into two binomials. So I'm gonna open two sets of empty parentheses so I can fill them with the terms needed to have a factorization. The first term in each set of parentheses will come from the first term in the trinomial. So the first term in our trinomial is S squared. So the two things that would multiply together to give us S squared are going to be S and S. So in my parentheses, S is the first term in each of them. Next, I need to find two values that not only multiply to positive 77 but add to positive 18, noting that both are positive, I'm gonna put plus signs next to the s in my binomials. So in my parentheses, I have S plus for both sets parentheses because only two positives can add to a positive and multiply to a positive. So my options on things that will multiply to 77. Well, I'm gonna check 1 times 77 that does M multiply to 77, but it will not add to 18. So my next option would be seven and 11 when I do seven multiplied by 11, I get 77 when I do seven added to 11, I get 18. So 7 and 11 sound like the values that are gonna work. So currently my parentheses are parentheses. S plus seven multiplied by the parentheses. S plus 11. This is likely my factorization, but we have been asked to check first. So we're gonna check it using the foil method. Recall that foil stands for first, outer, inner and last. And that's the order we're gonna multiply our values. So from my binomials, the first terms are S and S multiplying them together, I get S squared outer would be S multiplied by 11 and that will give me a positive 11. S inner would be seven multiplied by S which gives me a positive 7 s and last positive seven multiplied by positive 11, which gives me a positive 77. I now have S squared plus 11 S plus seven S plus 77. I'm gonna combine my like terms of 11 s and 7 s and when I do, my expression will be S squared plus 18 S plus 77. This does match my original trinomial. So that means that this factorization checks and is our solution. So our solution is the parentheses S plus seven multiplied by the parentheses S plus 11. And that matches answer choice A have a nice day.

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication.y² + 10y + 16

Key Concepts

Factoring Trinomials

Prime Trinomials

FOIL Method

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