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. Calculate the discriminant using the formula D=b2−4*a*c to determine if the expression can be factored over the real numbers.

D=(−2)2−4*(1)*(4)

D=4−16

D=−12

3. Conclude that since the discriminant is negative (D<0, the quadratic has no real roots and cannot be factored into linear factors using real numbers.

4. Apply the quadratic formula x=(−b±√(,D))/(2*a) to find the complex roots if factoring over the complex numbers is required.

x=(−(−2)±√(,−12))/(2*(1))

x=(2±2*i√(,3))/2

x=1±i√(,3)

5. Write the factored form using the complex roots (r_1)=1+i√(,3) and (r_2)=1−i√(,3) in the form (x−(r_1))*(x−(r_2))

(x−(1+i√(,3)))*(x−(1−i√(,3)))

Final Answer

x2−2*x+4=(x−1−i√(,3))*(x−1+i√(,3))

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