Factor x^2-4x+2

Problem

x2−4*x+2

Solution

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

2. Check for rational roots by testing if the discriminant D=b2−4*a*c is a perfect square.

D=(−4)2−4*(1)*(2)

D=16−8

D=8

3. Determine the roots using the quadratic formula x=(−b±√(,D))/(2*a) since the discriminant is not a perfect square.

x=(4±√(,8))/(2*(1))

x=(4±2√(,2))/2

x=2±√(,2)

4. Apply the factor theorem which states that if (r_1) and (r_2) are roots, the factored form is a*(x−(r_1))*(x−(r_2))

x2−4*x+2=(x−(2+√(,2)))*(x−(2−√(,2)))

5. Simplify the signs within the binomial factors.

x2−4*x+2=(x−2−√(,2))*(x−2+√(,2))

Final Answer

x2−4*x+2=(x−2−√(,2))*(x−2+√(,2))

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