Answer
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Step 1:I'll solve this step-by-step using polynomial factoring techniques:
Step 2:: Identify the polynomial
- Here, $$a = 1$$, $$b = -1$$, and $$c = -2
- This is a standard quadratic in the form ax^{2} + bx + c
Step 3:: Find two numbers that multiply to ac and add to b
* $$2 + (-3) = -1
- We need to find two numbers that: - By testing, we find 2 and - 3 work:
Step 4:: Rewrite the middle term using these numbers
x^{2} - x - 2 = x^{2} + 2x - 3x - 2
Step 5:: Group the terms
(x^{2} + 2x) + (-3x - 2)
Step 6:: Factor by grouping
x(x + 2) - 1(3x + 2)
Step 7:: Factor out the common terms
(x - 1)(x + 2)
Final Answer
x^{2} - x - 2 = (x - 1)(x + 2)
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