Factor 12x^2-128x+256

Problem

12*x2−128*x+256

Solution

1. Factor out the greatest common factor (GCF) from all three terms, which is 4

4*(3*x2−32*x+64)

2. Identify the coefficients of the quadratic expression inside the parentheses, where a=3 b=−32 and c=64

a⋅c=3⋅64=192

3. Find two numbers that multiply to 192 and add to −32 These numbers are −24 and −8

−24⋅−8=192

−24+(−8)=−32

4. Split the middle term −32*x using the two numbers found in the previous step.

4*(3*x2−24*x−8*x+64)

5. Factor by grouping the terms inside the parentheses.

4*(3*x*(x−8)−8*(x−8))

6. Factor out the common binomial (x−8) to complete the factorization.

4*(3*x−8)*(x−8)

Final Answer

12*x2−128*x+256=4*(3*x−8)*(x−8)

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