Factor 12x^2-64x+64

Problem

12*x2−64*x+64

Solution

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

4*(3*x2−16*x+16)

2. Identify the coefficients of the quadratic expression inside the parentheses, a*x2+b*x+c where a=3 b=−16 and c=16

a⋅c=3⋅16=48

3. Find two numbers that multiply to 48 and add to −16 These numbers are −12 and −4

−12⋅−4=48

−12+(−4)=−16

4. Split the middle term −16*x using the numbers found in the previous step.

4*(3*x2−12*x−4*x+16)

5. Factor by grouping the terms inside the parentheses.

4*((3*x2−12*x)+(−4*x+16))

6. Factor out the GCF from each group.

4*(3*x*(x−4)−4*(x−4))

7. Factor out the common binomial (x−4)

4*(3*x−4)*(x−4)

Final Answer

12*x2−64*x+64=4*(3*x−4)*(x−4)

Want more problems? Check here!