Factor x^2-2x-4

Problem

x2−2*x−4

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=−2 and c=−4

2. Check for rational roots by looking for two integers that multiply to a*c=−4 and add to b=−2 Since no such integers exist, the expression cannot be factored over the integers.

3. Find the roots using the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a)

4. Substitute the values into the formula:

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

5. Simplify the expression under the radical:

x=(2±√(,4+16))/2

x=(2±√(,20))/2

6. Simplify the radical √(,20)=√(,4⋅5)=2√(,5)

x=(2±2√(,5))/2

x=1±√(,5)

7. Write the factors using the roots (r_1)=1+√(,5) and (r_2)=1−√(,5) in the form (x−(r_1))*(x−(r_2))

Final Answer

x2−2*x−4=(x−(1+√(,5)))*(x−(1−√(,5)))

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