3(x)2 - 125x + 1300

Question

find factors

Answer 1

3x^2 - 125x + 1300

It's a 3 on the x^2.  3 only factors to 3 and 1, so the answer should look like this:

(3x  )(x  )

How does 1300 factor? What does 3 * one number plus 3 * the other number look like?

100 * 13, 313, 139
50 * 26, 176, 128
25 * 52, 127, 181
10 * 130, 160, 400
20 * 65, 125, 215

Ah, there's our middle term- the 125.  So our answer should look like this:

(3x  65)(x  20)

The 125 is a -, so the answer should look like this:

(3x - 65) (x - 20)

Check that by expanding it, see if we get the original problem:

3x^2 - 60x - 65x + 1300

3x^2 - 125x + 1300

We get the original problem, so the answer checks out.

Answer:  (3x-65)(x-20)