In order to factor  , first we need to ask ourselves: What two numbers multiply to 8 and add to -6? 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
(-1)*(-8)=8
(-2)*(-4)=8
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6
| First Number | | | Second Number | | | Sum | | 1 | | | 8 | || | 1+8=9 | | 2 | | | 4 | || | 2+4=6 | | -1 | | | -8 | || | -1+(-8)=-9 | | -2 | | | -4 | || | -2+(-4)=-6 | We can see from the table that -2 and -4 add to -6.So the two numbers that multiply to 8 and add to -6 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
So in other words,  factors to 
Now set each factor equal to zero:
 Solve for x
 Solve for x
So our solution is x=2 and x=4
b)
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=4 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 4, 2.
Here's your graph:
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So our solution is x=2, and x=4.
Notice how we got the same answer but took another route to get there.
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