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Chapter 6: Problem 28

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$w^{2}+12 w-64$$

Short Answer

Expert verified
The factorization of the trinomial \(w^{2} + 12w - 64\) is \((w - 4)(w + 16)\).

Step by step solution

01

Identify the Form of the Trinomial

The trinomial is in the form \(ax^{2} + bx + c\) where \(a = 1, b = 12, and c = -64\). The goal is to find two numbers that multiply to \(c\) and add up to \(b\).
02

Identify the Factors

The numbers 16 and -4 are suitable because 16 times -4 equals -64, and 16 plus -4 equals 12.
03

Write the Factorization

Therefore, the trinomial \(w^{2} + 12w - 64\) can be factorized as \((w - 4)(w + 16)\).
04

Check by Multiplying

Check this factorization using FOIL multiplication. If the factors are correct, they will multiply back into the original trinomial: \((w - 4)(w + 16) = w^2 + 16w - 4w - 64 = w^2 + 12w - 64\). Thus, the factorization is correct.

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Most popular questions from this chapter

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