Hey everyone!
Yesterday I had a math test and got 90% on it. Definitely happy but one question I couldn't solve even tough I knew how to do it...

Let me explain. Please note that English isn't my first language so I might get some words wrong. Also please note that I'm self-learning all math, so the way I solve or write might not be official.

So let's say you need to put the next problem between brackets.

x² +2x -15

I'd solve it like this.

-15 = 1 • -15, -15 • 1, 3 • -5, -5 • 3, -3 • 5 etc

+2x = -3 + 5

Solution x² +2x -15 = (x -3)(x +5)

So I actually know how to solve it. Now my test yesterday threw a curve ball by not having a number before the second x...

It was like this: x² -x -20

I got totally confused because how do I calculate x from -20 like I did in the example I gave? I couldn't because I need to have a number before the x right?

If anyone could explain this to me I'd be very happy!

Thanks!
> I'd solve it like this. -15 = 1 • -15, -15 • 1, 3 • -5, -5 • 3, -3 • 5 etc +2x = -3 + 5

Guessing factors is a perfectly valid way of finding them (just so long as they are integers).

You can also use that technique here. What two numbers when multiplied together are -20 but when added together are -1?

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^(aside: it's not  *solve* but *factorise*. Solving is when you get something like x=5 at the end.)
When you have no coefficient, it's the same as just having a coefficient of 1. So you think of it as being

x^(2) \+ (-1)x + (-20)

And think of two numbers that add to -1 but multiply to -20.
Thank you all! I love this so much! Allways loved math never had understood this before and now I did!
I didn’t know we could do this!
It feels as if my brain just opened up

a huge space!
A trick is that "for every polynomial with integer coefficients, IF that poly has an integer root then that root divides the constant term"
Why not use the quadratic formula? The solutions you get from it (x1 and x2) are what you put in the brackets as (x-x1)(x-x2), i believe it's faster than guessing integers
That's the neat thing, there is a number before the x, and it's -1.

A*B = -20
A+B = -1

Edit sp.