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

#1**+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 - 1x - 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

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

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