Question

Can someone please help me with factoring?
I just need a explanation of the topic. I got GCF and how to find it down, what about
http://prntscr.com/c169c9
How do I do that?

Answer 1

@Jadeishere

Answer 2

Those are quadratic equations, familiar with those?

Answer 3

Kay, Would you care to know a simple way to do this?

Answer 4

Yes please

Answer 5

Awesome :)

There are many ways to do this, but we're going a very, very simple route.
The first equation is \[x^2 - 4x - 12\]

Make a T chart

Answer 6

Ok, got that.

Answer 7

We have an overlap in numbers, -6 and +2
Those numbers will be our factors

(x - 6)( x + 2) or (x + 2)(x - 6)

Those two are the same :)

Get it?

Answer 8

All you're doing is finding numbers that add up to the middle term and have a product that is equal to the last term

(x + a)(x + b)
x^2 + bx + ax + ab

Answer 9

Yes tha makes since

Answer 10

You want to try one yourself?

Answer 11

Is the 4th one Prime?

Answer 12

Yes, it is, but do you know why?

Answer 13

Because there is no common factors?

Answer 14

Not quite. They have 3 and 4 in common

BUT

-3 + 4 = 1 -3 * 4 = -12
-3 + -4 = -7 -3 * -4 = POSITIVE 12
-4 + 3 = -1 -4 * 3 = -12
4 + 3 = 7 4 * 3 = 12


So there is no way for the factors to equal 7 when added together, or multiply to equal 12

Answer 15

Wait, 3 nor 4 goes into 7...

Answer 16

?

Answer 17

The 4th one. -7x - 12 am I only factoring 12?

Answer 18

You're factoring for both, but no factors of 3 and 4, negative or positive, can equal -7 and -12

Answer 19

Ok so how does the 3rd one work?

Answer 20

Okay, the third one you're looking for two numbers that multiply to -12 but add to -1

Answer 21

How do I know when to do that?

Answer 22

What do you mean?

Answer 23

When to add? Or is that every time?

Answer 24

Can I say something?

Answer 25

Of course! Any input is welcome :)

Answer 26

Do I add it up every time? Like the third number needs factors and the factors have to add up to -1 right? Or for other equations its whatever in front of the x?

Answer 27

To me, 12 = 1*12
12 = 2*6
12= 3*4
We need choose 1 pair to work with. But which one?
1 and 12, there is no way to add or subtract them together to get 4. Hence, 1 and 12 is rejected.
Same as 3 and 4
Now, for 2 and 6 . We see that 6-2 = 4 and -6+2 =-4. That is the potential candidate.
(We need -4, right?)
Hence the factors are (x-6)(x+2)
done.

Answer 28

Why do we need -4?

Answer 29

How do I find -4 and know thats what I need to add up?

Answer 30

Pretty much what @Loser66 said Oswald

But, not all people are able to function that way >.<

Answer 31

@OswaldMurphy I'm a bit out-of-the-sorts, would you mind explaining what you're asking?

Answer 32

because \(x^2 \color{red}{-}4-12\)

Answer 33

What do you mean by finding -4?