Question

How do you factor trinomials?

Answer 1

Extension to factoring, when the trinomials do not factor into a square (it also works with squares).

Sum-product-method
Say you have an expression like `x^2+15x+36`
Then you try to write `36` as the product of two numbers, and `15` as the sum (or difference) of the same two numbers. In this case (with both being positive) it's not so hard. You take the sum.

You can write `36=1*36=2*18=3*12=4*9=6*6`
Sums of these are `37,20,15,13,12` respectively
Differences are `35,16,9,5,0` respectively
`15=+3+12` will do. So the factoring becomes:
`(x+3)(x+12)`
Check your answer! `=x^2+12x+3x+36`

It's a bit harder when one or two of the numbers are negative, let's take `x^2-15x+36`
Same as the first, only now both factors are negative
`(x-3)(x-12)=x^2-12x-3x+36=` the original

Extra
If the last number (`36`) is negative, you will have to work with the difference of the factors. Check the next one yourself:
`x^2+5x-36=(x+9)(x-4)=?`

And now try: `x^2-5x-36=?`