To factor quadratics, you multiply a and c, and find the factors that when added equal b...
3x^2+5x+2
3(2)=6
Factors of 6 are
-1 and -6
-2 and -3
1 and 6
2 and 3
2 +3= 5(which is the b value)
Then you split 5x into 3x and 2x
3x^2+3x+2x+2
Group them together
(3x^2+3x) + (2x+2)
Take out anything in common
3x(x+1)+2(x+1)
Since the equations in the parentheses are the same, you can combine the terms on the outside to be 1
(x+1)(3x+2)
That is 3x^2+5x+2 factored out.
For the other equation you follow the same steps.
3(-12)=-36
-36
-1 and 36
-2 and 18
-3 and 12
-4 and 9
3x^2+9x-4x-12
(3x^2+9x)+(-4x-12)
3x(x+3)-4(x+3)
(3x-4)(x+3)
That is 3x^2+5x-12 factored.
