## Factoring a Quadractic Equation x^2-2x-2

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

### Factoring a Quadractic Equation x^2-2x-2

I seem to be having a problem when factoring this. Though I already know what the answer is, I'm confused on how that answer is actually gotten.

Equation: x^2-2x-2

First, I try finding a product sum answer that will fullfill the requirments - when multiplied together equal -2 and when added together equal -2.

And this is where the problem sets in. The only possible number combination is 2 and 1, because they need to equal 2 when multiplied together. But there is no way to do this without having their sum be -3, -1, 1, or 3.

This is just made more complicated by the fact that the factor is (x-3)(x+1), or at least that's what I figure from the graph since it has zeroes of 3 and -1.

Any idea what I could be doing wrong here?
Aqua Dragon

Posts: 10
Joined: Sat Apr 11, 2009 3:44 pm

Aqua Dragon wrote:I seem to be having a problem when factoring this.

Expression: x^2-2x-2

...it has zeroes of 3 and -1.

If x = 3 and x = -1 are zeroes of the associated function equation y = x2 - 2x - 2, then, by definition, you'll get zero when you plug these values in for x. Do you?

. . . . .(3)2 - 2(3) - 2 = 9 - 6 - 2 = 9 - 8 = 1

. . . . .(-1)2 - 2(-1) - 2 = 1 + 2 - 2 = 1

Neither value is a zero. In fact, if you set the quadratic expression equal to zero and then apply the Quadratic Formula, you will see why you're having trouble factoring. The zeroes are actually:

. . . . .$1\, \pm\, \sqrt{3}$