SOLUTION: Factor completely and show a detailed solution (2x^2 - 4x + 1)^2 - 14x^2 + 28x + 3

Algebra ->  Finance -> SOLUTION: Factor completely and show a detailed solution (2x^2 - 4x + 1)^2 - 14x^2 + 28x + 3      Log On


   

Question 1040174: Factor completely and show a detailed solution
(2x^2 - 4x + 1)^2 - 14x^2 + 28x + 3
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let y be y=2x%5E2-4x%2B1 .
We can re-write the original expression as
y%5E2-7y%2B10=%28y-5%29%28y-2%29 .
Since y=2x%5E2-4x%2B1 , system%28y-5=2x%5E2-4x-4%2C%22and%22%2Cy-2=2x%5E2-4x-1%29 , so
highlight%28%282x%5E2-4x%2B1%29%5E2-14x%5E2%2B28x%2B3=%282x%5E2-4x-4%29%282x%5E2-4x-1%29%29 .
That is as far as we can go, unless we use ugly irrational coefficients,
because all the zeros of 2x%5E2-4x-4 and 2x%5E2-4x-1 are irrational numbers.