How do I factor (x^2-2x-1)? Is it prime?

Question

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Answer 1

This equation is not factorable. If you want to solve for x, you'll need to use the quadratic formula.

Answer 2

Using the quadratic formula, you get

x = (2+/-√(4+4))/2 = 1 +/- √(2)

So that means the expression DOES factor, but its roots are irrational. The factored form would therefore be:

(x - 1 + √(2))(x - 1 - √(2))

Every quadratic expression is factorable (even those with complex roots). When you can't factor with normal factoring techniques, you have to use the quadratic formula to discover the roots that you need for the factored form.

This may be more information than you wanted, but I couldn't let stand the assertions that this expression can't be factored.

Answer 3

You can use the quadratic formula to solve this or use completion of squares.

x^2 - 2x - 1
= x^2 - 2x + 1 - 2
= (x-1)^2 - [√2]^2
= (x-1+√2)(x-1-√2)

Answer 4

The factors are (2+sqrt(5)/)2, (2-sqrt(5)/)2. It's not "prime" but the roots are irrational.

Answer 5

Well it has a minimum at x=1,y=-2 and cuts the x axis either side of this value. So must have factors.

Answer 6

quadratic formula. hint it is NOT prime

x=2+/- sq root{8}

two plus or minus the square root of eight

Answer 7

its not factorable.
if it was +1 then its factorable.

you have to use the quadratic formula for it

Answer 8

use

Quadratic Formula
a=2 b=-2 c=-1
x = - b ± √ (b² - 4ac) / 2a

Answer 9

its prime;
you can't factor it

Answer 10

im pretty sure its prime =]