Question

Show your work for factoring or quadratic formula:

Answer 1

First, I'd simplify this problem by dividing every term by 2:

x^4 - 4x^3 + 5x^2 - 4x + 4 = 0

Then I'd think of the possible factors of that constant term, 4:  They would be plus or minus 1, plus or minus 2, or plus or minus 4.

Let's try x = -4 as a possible root.  Setting up and using synthetic division:

      ____________________
-4  /   1   -4   5    -4    4
              -4   32
     ----------------------------
         1    -8  37

This result is not helpful.  So, try the possible root +4 instead:
       ________________
+4  /   1   -4   5    -4    4
                4    0   20   64
       ----------------------------
         1     0    5    16   68             4 is not a root because the remainder   
                                                    (68) is not zero.

Try x = 2:

       ________________
+2  /   1   -4   5    -4    4
                2   -4    2    -40
       ----------------------------
          1    -2   1    -2    0

2 is a root because the remainder is zero.

Continue this process until you've found the other 3 roots.

Hint:  Try  the possible root x = -2 with the following coefficients:

     ____________
-2 /  1   -2   1   -2

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