Factor x^2-2x+5

Problem

x2−2*x+5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=−2 and c=5

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)*(5)

D=4−20

D=−16

3. Determine the roots using the quadratic formula x=(−b±√(,D))/(2*a) since the discriminant is negative, indicating complex roots.

x=(−(−2)±√(,−16))/(2*(1))

x=(2±4*i)/2

x=1±2*i

4. Apply the factor theorem which states that if r is a root, then (x−r) is a factor.

x2−2*x+5=(x−(1+2*i))*(x−(1−2*i))

5. Simplify the signs within the factors.

x2−2*x+5=(x−1−2*i)*(x−1+2*i)

Final Answer

x2−2*x+5=(x−1−2*i)*(x−1+2*i)

Want more problems? Check here!