Question

How do you factor the trinomial `x^2+2x-4=0`?

Answer 1

`y = (x + 1 + sqrt5)(x + 1 - sqrt5)`

Explanation:

Method 1.
Apply the formula of quadratic function in intercept form (Google Search):
`y = (x +b/(2a) + d/(2a))(x + b/(2a) - d/(2a))`, with
`b/(2a )= 1`
`D = d^2 = 4 + 16 = 20` --> `d = +- 2sqrt5`
We get:
`y = (x + 1 + sqrt5)(x + 1 - sqrt5)`
Method 2.
Solve the quadratic equation.
`D = d^2 = 4 + 16 = 20` --> `d = +- 2sqrt5`
2 real roots: `x1 = (- 1 - sqrt5)` and `x2 = (- 1 + sqrt5)`
Therefor, the factored form is:
`y = (x - x1)(x - x2) = (x + 1 + sqrt5)(x + 1 - sqrt5)`