Problem 27 - Introductory Algebra for College Students

Question

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$w^{2}-30 w-64$$

Step-by-Step Solution

Answer

The factors of the given trinomial \(w^{2}-30 w-64\) are \((w-32) \text{ and } (w+2)\).

Step 1: Set up Pair of Parentheses

Start by setting up a pair of parentheses with the variable in each: \((w \ ) \cdot (w \ ).\)

Step 2: Find Factors

Now, try to find the two numbers that multiply to -64 and add up to -30. The numbers -32 and 2 satisfy these conditions. Therefore, the factors of the trinomial are \((w-32) \text{ and } (w+2)\).

Step 3: Verify the Factorization

Now we need to verify these factors by applying FOIL multiplication. When the factors are multiplied using the FOIL method, \((w-32) \times (w+2) = w^{2}-30w-64\), it results to be the same as the initial trinomial, hence confirming our solution.