Factor x^2-3x-54

Problem

x2−3*x−54

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−3 and c=−54

2. Find two numbers that multiply to the constant term c=−54 and add to the linear coefficient b=−3

3. Determine the pair of numbers by testing factors of −54 The numbers 6 and −9 satisfy both conditions because 6⋅(−9)=−54 and 6 + (-9) = -3$.

4. Write the factored form using these numbers as (x+p)*(x+q)

Final Answer

x2−3*x−54=(x+6)*(x−9)

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