Question

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

Answer 1

`(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.