Factor 36x^2-54x-36

Problem

36*x2−54*x−36

Solution

1. Identify the greatest common factor (GCF) for all three terms. The numbers 36 54 and 36 are all divisible by 18

18*(2*x2−3*x−2)

2. Factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to 2⋅(−2)=−4 and add to −3 These numbers are −4 and 1

2*x2−4*x+x−2

3. Factor by grouping the terms within the parentheses.

2*x*(x−2)+1*(x−2)

4. Extract the common binomial factor (x−2) from the expression.

(2*x+1)*(x−2)

5. Combine all factors to write the final factored form of the original expression.

18*(2*x+1)*(x−2)

Final Answer

36*x2−54*x−36=18*(2*x+1)*(x−2)

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