Factor x^2-2x-2

Problem

x2−2*x−2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=−2 and c=−2

2. Check for rational roots by looking for two numbers that multiply to c=−2 and add to b=−2 Since no such integers exist, use the quadratic formula to find the roots.

3. Apply the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a) to find the zeros of the expression.

x=(−(−2)±√(,(−2)2−4*(1)*(−2)))/(2*(1))

4. Simplify the expression under the radical and solve for x

x=(2±√(,4+8))/2

x=(2±√(,12))/2

x=(2±2√(,3))/2

x=1±√(,3)

5. Write the factors using the roots (x_1)=1+√(,3) and (x_2)=1−√(,3) in the form (x−(x_1))*(x−(x_2))

(x−(1+√(,3)))*(x−(1−√(,3)))

6. Distribute the negative signs within the parentheses to reach the final factored form.

(x−1−√(,3))*(x−1+√(,3))

Final Answer

x2−2*x−2=(x−1−√(,3))*(x−1+√(,3))

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