How do you factor 2x2 plus 7x plus 6?

axx+bx+c 2xx+7x+6

a=2

b=7

c=6

Multiply a and c:

2*6=12

Find multiples of ac that add up to b (d,e [ie de=ac, d+e=b]):

12=2*2*3

12=4*3, -4*-3

12=6*2, -6*-2

Rewrite axx+bx+c into axx+dx+ex+c:

2xx+7x+6

2xx+4x+3x+6

Factor sets of terms (ie axx+dx, and ex+c):

2xx+4x+3x+6

2x(x+2)+3(x+2)

Combine like terms:

2x(x+2)+3(x+2)

(x+2)(2x+3)