Question

Is it possible to factor `y=2x^2 -452x-68`? If so, what are the factors?

Answer 1

`y=2(x-113+sqrt(12803))(x-113-sqrt(12803))`

Explanation:

Step 1: Removing the obvious integer common factor:
`color(white)("XXX")y=2(x^2-226-35)`

From this point on there are no "pretty" factors but...
Step 2: Use the quadratic formula to find the roots

For the general quadratic: `ax^2+bx+c` the roots are given by:
`color(white)("XXX")x=(-b+-sqrt(b^2-4ac))/(2a)`

In this case
`color(white)("XXX")x=(226+-sqrt((-226)^2-4(1)(-35)))/(2(1))`

`color(white)("XXXXXX")=(226+-sqrt(51212))/2 = 113+-sqrt(12803)`

So we can continue the factoring as:
`color(white)("XXX")y=2(x-113+sqrt(12803))(x-113-sqrt(12803))`