Question

How do you factor `x^2 - 4x - 2`?

Answer 1

Use the quadratic formula to get:
`color(white)("XXX")(x-2+sqrt(6))(x-2-sqrt(6))`

Explanation:

For a quadratic expression:
`ax^2+bx+c`
the zeros of the expression are given by the formula
`color(white)("XXX")x_z=(-b+-sqrt(b^2-4ac))/(2a)`

For the given expression
`color(white)("XXX")a=1`
`color(white)("XXX")b=-4`
`color(white)("XXX")c=-2`

So
`color(white)("XXX")x_z = (4+-sqrt((-4)^2+4(1)(-2)))/(2(1))`

`color(white)("XXX")=(4+sqrt(16+8))/(2)`

`color(white)("XXX")=(4+-2sqrt(6))/2`

`color(white)("XXX")=2+-sqrt(6)`

If `x_(z1) and x_(z2)` are zeros of a quadratic then the quadratic can be factored as:
`color(white)("XXX")(x-x_(z1))(x-x_(z2))`