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. Check for real roots by calculating the discriminant D=b2−4*a*c

3. Calculate the discriminant: D=2−4*(1)*(5)=4−20=−16

4. Determine the nature of the factors. Since the discriminant is negative, the expression cannot be factored using real numbers.

5. Apply the quadratic formula to find complex roots: x=(−b±√(,D))/(2*a)

6. Substitute the values: x=(−2±√(,−16))/(2*(1))

7. Simplify the square root of the negative number: x=(−2±4*i)/2

8. Divide by 2 to find the roots: x=−1+2*i and x=−1−2*i

9. Write the factors in the form (x−(r_1))*(x−(r_2))

Final Answer

x2+2*x+5=(x−(−1+2*i))*(x−(−1−2*i))

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