SOLUTION: Factor - x2 - 10x - 56

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Question 76766: Factor - x2 - 10x - 56
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First factor out a negative 1
-1%28x%5E2%2B10x%2B56%29
Now factor the quadratic in the parenthesis:
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B10%2Ax%2B56, first we need to ask ourselves: What two numbers multiply to 56 and add to 10? Lets find out by listing all of the possible factors of 56


Factors:

1,2,4,7,8,14,28,56,

-1,-2,-4,-7,-8,-14,-28,-56,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 56.

1*56=56

2*28=56

4*14=56

7*8=56

(-1)*(-56)=56

(-2)*(-28)=56

(-4)*(-14)=56

(-7)*(-8)=56

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 10

||||||||
First Number|Second Number|Sum
1|56|1+56=57
2|28|2+28=30
4|14|4+14=18
7|8|7+8=15
-1|-56|-1+(-56)=-57
-2|-28|-2+(-28)=-30
-4|-14|-4+(-14)=-18
-7|-8|-7+(-8)=-15
substitute a=3 and b=7 So the equation becomes: (x+3)(x+7) Notice that if we foil (x+3)(x+7) we get the quadratic 1%2Ax%5E2%2B10%2Ax%2B56 again None of these factors add to 10. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.


So the quadratic -x%5E2-10x-56 cannot be factored