+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
+128460 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 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
+314 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.
