SOLUTION: Find the zero of (f), identify all multiple zeros for (x-4) to the third power minus 4(x-4)

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Question 1001661: Find the zero of (f), identify all multiple zeros for (x-4) to the third power minus 4(x-4)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x-4%29%5E3-4%28x-4%29
From here, x=4 would make the function equal 0. Degree 3 for x in the function definition. It appears to be the only zero for the function, or at least the only real zerol

f%28x%29=%28x-4%29%28%28x-4%29%5E2-4%29

Do the full multiplying to get general form, and it is x%5E3-12x%5E2%2B44x-48.

Test the root of 4 using synthetic division, and the resulting quotient is x%5E2-8x%2B12 which is factorable...

The fully factorized function is therefore highlight%28%28x-4%29%28x-6%29%28x-2%29%29. The roots or zeros are 4, 6, and 2, each of multiplicity ONE.