Factor x^2+7x+12

Problem

x2+7*x+12

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=7 and c=12

2. Find two numbers that multiply to c (12) and add to b (7).

3. Determine the factors of 12: (1,12) (2,6) and (3,4)

4. Select the pair (3,4) because 3×4=12 and 3 + 4 = 7$.

5. Write the expression in factored form (x+p)*(x+q) using the identified numbers.

Final Answer

x2+7*x+12=(x+3)*(x+4)

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