Factor x^2+15x+56

Problem

x2+15*x+56

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=15 and c=56

2. Find two integers that multiply to the constant term c=56 and add up to the linear coefficient b=15

3. List the factor pairs of 56 (1,56) (2,28) (4,14) and (7,8)

4. Select the pair (7,8) because 7×8=56 and 7 + 8 = 15$.

5. Write the factored form using these integers as (x+p)*(x+q)

Final Answer

x2+15*x+56=(x+7)*(x+8)

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