Factor x^2+2x+48

Problem

x2+2*x+48

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=2 and c=48

2. Search for two integers that multiply to c=48 and add to b=2

3. List the factor pairs of 48: (1,48) (2,24) (3,16) (4,12) and (6,8)

4. Check the sums of these pairs: 1+48=49 2+24=26 3+16=19 4+12=16 and 6+8=14

5. Determine if the expression is factorable over the integers. Since no pair of integers sums to 2, the quadratic cannot be factored into the form (x+p)*(x+q) using rational numbers.

6. Conclude that the expression is irreducible over the integers, also known as a prime polynomial.

Final Answer

x2+2*x+48=prime polynomial

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