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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!
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> 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.)
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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.
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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!
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A trick is that "for every polynomial with integer coefficients, IF that poly has an integer root then that root divides the constant term"
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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
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That's the neat thing, there is a number before the x, and it's -1.

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

Edit sp.
ago

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