SOLUTION: how to factor x^2 - x - 10 ?

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Question 846329: how to factor x^2 - x - 10 ?
Answer by josgarithmetic(39797) About Me  (Show Source):
You can put this solution on YOUR website!
This is not a square trinomial: highlight_green%28x%5E2+-+x+-+10%29.

It also appears to not be factorable.
The usual choices for checking integers would be 1 and 10; or 2 and 5. Any of those pair, regardless of sign choice, will NOT give the -1 and the -10 required.

Discriminant: %28-1%29%5E2-4%28-10%29=1%2B40=highlight_green%2841%29.

Zeros at x=%281-sqrt%2841%29%29%2F2 and x=%281%2Bsqrt%2841%29%29%2F2.

The given quadratic trinomial is not factorable into two linear binomials; but if you really want, you can factor into binomials having the shown irrational constant terms. If you were looking for something simpler, then any simpler factorization is not possible.

This is the factorization:
%28x-%281-sqrt%2841%29%29%2F2%29%28x-%281%2Bsqrt%2841%29%29%2F2%29