How do you factor: #y=x^2 - 5#?

1 Answer
Dec 23, 2015

Answer:

Apply the difference of squares formula to find that
#x^2 - 5 = (x + sqrt(5))(x - sqrt(5))#

Explanation:

The difference of squares formula states that
#a^2 - b^2 = (a+b)(a-b)#
(This is easy to verify by expanding the right hand side)

While #5# may not be a perfect square, it is still the square of something... specifically, it is the square of #sqrt(5)#
Then, applying the formula, we have

#x^2 - 5 = x^2 - (sqrt(5))^2 = (x + sqrt(5))(x - sqrt(5))#