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Chapter 6: Problem 15

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}+10 y-39$$

Short Answer

Expert verified
The factored form of the trinomial \(y^{2}+10y-39\) is \((y-3)(y+13)\).

Step by step solution

01

Identify the trinomial

The given trinomial is \(y^{2}+10y-39\). The goal is to find factors \(m\) and \(n\), of the term \(-39\) that sum to \(10\).
02

Factor the trinomial

The factors of \(-39\) that add up to \(10\) are \(-3\) and \(13\). Therefore, the trinomial can be factored to \((y-3)(y+13)\).
03

Check the factorization using FOIL method

We validate by using the FOIL method: First terms: \(y*y = y^{2}\), Outer terms: \(y*13 = 13y\), Inner terms: \(-3*y = -3y\), Last terms: \(-3*13 = -39\). Summing these up: \(y^{2} + 13y - 3y - 39 = y^{2} + 10y - 39\), which is indeed the original trinomial. So, the factorization is correct and the check is successful.

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Most popular questions from this chapter

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$9 x^{4}+18 x^{3}+6 x^{2}$$

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