Use synthetic division to solve these problems
5 | 1 -4 -7 10
| v 5 5 -10
1 1 -2 0
This leads to x^2+x-2
Next we find what adds to 1 and multiplies to -2
The factors of f(x) are 2 and -1, written out as (x+2) and (x-1)
-1/2 | 2 3 -23 -12
| v -1 -1 12
2 2 -24 0
This leads to 2x^2+2x-24
Next, multiply the 2 from the a value (since a is the value with x^2 and c is the value without any x) with -24, which is -48
Now find what adds to 2 and multiplies to -48
The values for this are 8 and -6, but keep in mind, when multiplying the value of a by c, you now have to add the values in place of what you tried adding it to, this time in the problem we found using synthetic division, in this case the 2 in the b value (the middle of the equation, or the value with only one x)
2x^2+8x-6x-24
When group factoring, you'd get 2x(x+4) -6 (x+4)
So, the factors of g(x) are (x+4) and (2x-6)
