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

1 Answer
Alan P.
Feb 10, 2016

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))

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