How do you factor w^ { 2} - 32- 4w?

1 Answer
Jun 14, 2017

(w-8)(w+4)

Explanation:

This equation is in general form, ax^2+bx+c=0

You are trying to find two factors that multiply together to be w^2-32-4w. It should look like this: (w+?)(w+?)

For visual purposes (and to match general form), I rearranged the polynomial:
w^2-4w-32

Using this as a reference: (w+?)(w+?)
The ?'s should ADD up to equal the b value, which is -4.
The ?'s should be MULTIPLIED to equal the c value, which is -32.

The simplest approach is to find all the FACTORS of -32.
Factors of -32: (32*-1); (-32*1); (16*-2); (-16*2); (8*-4); (-8*4)
I put them in pairs to help see the connections between the numbers.

For each pair, add the numbers together until you find a pair with a sum of -4.

You'll see that the pair (-8*4) works out to have a sum of -4.

Substitute -8 and 4 for the ?'s in (w+?)(w+?)

The answer is (w-8)(w+4).

It may seem tedious at first, but as you do more problems, you'll get the hang of it and won't have to list numbers out because you can do mental math.