In order to factor  , first we need to ask ourselves: What two numbers multiply to -8 and add to -2? Lets find out by listing all of the possible factors of -8
Factors:
1,2,4,8,
-1,-2,-4,-8,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -8.
(-1)*(8)=-8
(-2)*(4)=-8
Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2
| First Number | | | Second Number | | | Sum | | 1 | | | -8 | || | 1+(-8)=-7 | | 2 | | | -4 | || | 2+(-4)=-2 | | -1 | | | 8 | || | (-1)+8=7 | | -2 | | | 4 | || | (-2)+4=2 | We can see from the table that 2 and -4 add to -2.So the two numbers that multiply to -8 and add to -2 are: 2 and -4
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
 substitute a=2 and b=-4
So the equation becomes:
(x+2)(x-4)
Notice that if we foil (x+2)(x-4) we get the quadratic again
Now set each factor equal to zero
So our solution is:
or
|
|
(