We have:
14a^2-68a+48
We can first factor out the Largest Common Factor of 14, 68, and 48:
- 14 = 2xx7
- 68 = 2xx2xx17
- 48= 2xx2xx2xx2xx3
The Largest Common Factor is 2:
2(7a^2-34a+24)
Now we look for factors in the form of (ax+b)(cx+d) where
We know the factors for 7=7xx1, so let's set a=7, c=1
The factors for 24=-1xx-24, -2xx-12, -3xx-8, -4xx-6 (because ad+bc is a negative number and we've set ac to be positive, we need these factors to be negative).
Let's try some factors and trial and error our way into this:
acolor(white)(00000)bcolor(white)(0000)c color(white)(00000)dcolor(white)(000000)adcolor(white)(00000)bc color(white)(000)ad+bc
7color(white)(000)-8color(white)(000)1 color(white)(000)-3color(white)(000)-21color(white)(000)-8 color(white)(000)-29
7color(white)(000)-6color(white)(000)1 color(white)(000)-4color(white)(000)-28color(white)(000)-6 color(white)(000)-34
This gives us:
2(7a-6)(a-4)
