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 numbers that multiply to c (56 and add to b (−15.

3. Determine the factors by testing pairs of numbers that multiply to 56 −7 and −8

4. Verify the sum: −7+(−8)=−15 which matches the middle coefficient.

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

Final Answer

x2−15*x+56=(x−7)*(x−8)

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