Factor x^2+2x+24

Problem

x2+2*x+24

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c Here, a=1 b=2 and c=24

2. Determine the requirements for factoring. We need to find two numbers that multiply to c=24 and add to b=2

3. List the factor pairs of 24: (1,24) (2,12) (3,8) and (4,6)

4. Check the sums of these pairs: 1+24=25 2+12=14 3+8=11 and 4+6=10 None of these pairs sum to 2.

5. Evaluate the discriminant to check for real roots. The discriminant is D=b2−4*a*c

D=2−4*(1)*(24)

D=4−96

D=−92

6. Conclude that since the discriminant is negative, there are no real numbers that satisfy the conditions, and the expression cannot be factored over the set of real numbers using integers.

Final Answer

x2+2*x+24=is irreducible over the integers

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