+0  
 
+1
76
3
avatar+314 

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

ISmellGood  Sep 20, 2017
Sort: 

3+0 Answers

 #1
avatar+79671 
+3

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 

 

 

cool cool cool

CPhill  Sep 20, 2017
edited by CPhill  Sep 20, 2017
 #2
avatar+314 
+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
avatar+79671 
+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.....!!!!

 

 

cool cool cool

CPhill  Sep 20, 2017
edited by CPhill  Sep 20, 2017
edited by CPhill  Sep 20, 2017

18 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details