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Chapter 6: Problem 11

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$y^{2}-8 y+15$$

Short Answer

Expert verified
The factorization of the trinomial \(y^{2}-8 y+15\) is \((y-5)(y-3)\).

Step by step solution

01

Identify the Trinomial

The given trinomial is \(y^{2}-8 y+15\). We need to find two numbers that add to -8 (second term) and multiply to 15 (third term).
02

Factorize the Trinomial

Using the concept of number pairs, we find that the numbers -5 and -3 add up to -8 and multiply to 15. Therefore, the trinomial can be factored into \((y-5)(y-3)\).
03

Check the Factorization

To verify, we apply the FOIL method to this product: First: \(y*y =y^{2}\), Outer: \(-5*y = -5y\), Inner: \(-3*y = -3y\), Last: \(-5*-3 = 15\). Adding these four terms up gives \(y^{2} -5y - 3y + 15 = y^{2} -8 y+15\), which matches our initial trinomial, confirming that the factorization is correct.

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Most popular questions from this chapter

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$81 x^{4} y-y^{5}$$

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