Factor 12x^2-176x+484

Problem

12*x2−176*x+484

Solution

1. Identify the greatest common factor (GCF) for all three terms.

2. Factor out the GCF, which is 4

4*(3*x2−44*x+121)

3. Identify the coefficients of the quadratic expression inside the parentheses, where a=3 b=−44 and c=121

4. Find two numbers that multiply to a⋅c=3⋅121=363 and add to b=−44

5. Determine that the two numbers are −11 and −33

6. Rewrite the middle term −44*x using these two numbers.

4*(3*x2−33*x−11*x+121)

7. Factor by grouping the terms inside the parentheses.

4*(3*x*(x−11)−11*(x−11))

8. Factor out the common binomial (x−11)

4*(3*x−11)*(x−11)

Final Answer

12*x2−176*x+484=4*(3*x−11)*(x−11)

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