Factor x^2+2x+18

Problem

x2+2*x+18

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=2 and c=18

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

3. Evaluate the discriminant: D=2−4*(1)*(18)=4−72=−68

4. Conclude that since the discriminant is negative, the quadratic has no real roots and 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±√(,−68))/2

7. Simplify the square root: √(,−68)=√(,−1⋅4⋅17)=2*i√(,17)

8. Solve for x x=(−2±2*i√(,17))/2=−1±i√(,17)

9. Write the factors using the complex roots: (x−(−1+i√(,17)))*(x−(−1−i√(,17)))

Final Answer

x2+2*x+18=(x+1−i√(,17))*(x+1+i√(,17))

Want more problems? Check here!