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# STILL DONT GET IT

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I STILL don't understand factoring quadratics . I mean I understand when the question can be made into difference of squares but in other cases NOPE. Pls explain the problem below with detail and simply too. THANK YOU SOOO MUCH Sep 20, 2017

#1
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x^2 - x  - 12  = 0

Here's the way I do it .....this method applies only if the lead coefficient is an understood "1"...as in this case........

[ there are also other methods ]

Write this as

x^2  - 1 - 12  = 0

Now......   look  at  the term on  "x"   = -1

And look at the constant term  = -12

Ok....we  are looking for two integers that  multiply to  - 12   and  that  sum to - 1

Possibilities

1   -12

-1   12

2    -6

-2    6

3   - 4

-3    4

Notice that the only thing that works is   3  and - 4

(3) + ( - 4)    =  -1        and

(3) * (-4)  = -12

So....we just factor with these...i.e.,

(x  - 4)  ( x + 3)  = 0

Now.....set each factor to 0 and solve for  x....so we have.....

x  - 4  = 0                          and                        x + 3  = 0

add 4 to both sides                                    subtract 3 from both sides

x  = 4                                                             x  = -3

And those are the two solutions

The "smaller" x  = -3

The "larger" x  = 4

Does that help  ????

Try this one for yourself :      x^2  + 5x + 6  = 0   Sep 20, 2017
edited by CPhill  Sep 20, 2017
#2
+3

So first I find what sums to 5 and multiplies to 6.

2 3

-2 -3

1 6

-1 -6

2 and 3 equal to 5

(x+2)(x+3)=0

x can be either -2 or -3

DID I DO THAT RIGHT??? I think I did but idk.

ISmellGood  Sep 20, 2017
#3
+2

EXCELLENT, ISmellGood    !!!!!

I think you got the hang of it.....!!!!!~~~~

BTW -  you can check your answers...put either one back into the original equation...if you come up with "0"....you have done it correctly.....!!!!   Sep 20, 2017
edited by CPhill  Sep 20, 2017
edited by CPhill  Sep 20, 2017