Factor x^2+2x+56

Problem

x2+2*x+56

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c Here, a=1 b=2 and c=56

2. Determine if there are two integers that multiply to c (56 and add to b (2.

3. Analyze the discriminant D=b2−4*a*c to check for factorability over the set of real numbers.

D=2−4*(1)*(56)

D=4−224

D=−220

4. Conclude that since the discriminant is negative, the quadratic has no real roots and cannot be factored into linear binomials with real coefficients.

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

x=(−2±√(,−220))/2

x=(−2±2*i√(,55))/2

x=−1±i√(,55)

6. Write the factored form using the complex roots (r_1)=−1+i√(,55) and (r_2)=−1−i√(,55) in the form (x−(r_1))*(x−(r_2))

(x−(−1+i√(,55)))*(x−(−1−i√(,55)))

(x+1−i√(,55))*(x+1+i√(,55))

Final Answer

x2+2*x+56=(x+1−i√(,55))*(x+1+i√(,55))

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