How do you factor: y=x^2 - 5y=x2−5?

1 Answer
sente
Dec 23, 2015

Apply the difference of squares formula to find that
x^2 - 5 = (x + sqrt(5))(x - sqrt(5))x2−5=(x+√5)(x−√5)

Explanation:

The difference of squares formula states that
a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b)
(This is easy to verify by expanding the right hand side)

While 55 may not be a perfect square, it is still the square of something... specifically, it is the square of sqrt(5)√5
Then, applying the formula, we have

x^2 - 5 = x^2 - (sqrt(5))^2 = (x + sqrt(5))(x - sqrt(5))x2−5=x2−(√5)2=(x+√5)(x−√5)

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