Factor x^2+2x-1

Problem

x2+2*x−1

Solution

1. Identify the quadratic expression as being in the form a*x2+b*x+c where a=1 b=2 and c=−1

2. Check for rational roots by looking for two numbers that multiply to −1 and add to 2 Since no such integers exist, the expression cannot be factored over the integers.

3. Complete the square by adding and subtracting the square of half the linear coefficient, which is (2/2)2=1

x2+2*x+1−1−1

4. Group the perfect square trinomial and simplify the remaining constants.

(x2+2*x+1)−2

5. Rewrite the trinomial as a binomial square.

(x+1)2−2

6. Apply the difference of squares formula a2−b2=(a−b)*(a+b) where a=(x+1) and b=√(,2)

(x+1−√(,2))*(x+1+√(,2))

Final Answer

x2+2*x−1=(x+1−√(,2))*(x+1+√(,2))

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