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April 23, 2014

April 23, 2014

Posted by **Math 10** on Saturday, October 31, 2009 at 10:04pm.

x^2-2x-1

can u factor it? when i did it it couldn't be factored. i also dont know why it is not factorable because its a perfect square right?

please help me

- Sameul -
**jim**, Saturday, October 31, 2009 at 10:24pmIt can be factored, but not into integers like (x-1); more like sqrt(2)+-1, and it's definitely not a perfect square. I suspect you've got one of the signs backwards in your head, and you'll probably recognise that as we work through it.

Anyway, direct factorisation wasn't the question; this one is about completing the square.

Forget the constant for a minute, and focus on x^2-2x.

x^2-2x+c is a square. We just have to find c.

We know that

(x+a)^2 = x^2 + 2ax + a^2

and we want

x^2 - 2x + c

so, comparing the coefficients:

2a = -2

a = -1

(x-1)^2 = x^2 - 2x + 1

Our expression is 2 less than that, so:

x^2-2x-1 = (x-1)^2 - 2

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