SOLUTION: How to factor as a polynomial? x^2-5

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Question 76501: How to factor as a polynomial? x^2-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B0%2Ax%2B-5, first we need to ask ourselves: What two numbers multiply to -5 and add to 0? Lets find out by listing all of the possible factors of -5


Factors:

1,5,

-1,-5,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -5.

(-1)*(5)=-5

Now which of these pairs add to 0? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 0

||
First Number|Second Number|Sum
1|-5|1+(-5)=-4
-1|5|(-1)+5=4
None of these factors add to 0. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.