Question

Show your work for factoring or quadratic formula:

2x^4 - 8x^3 +10x^2 - 8x + 8 = 0



Please help, and possibly show the work. Thanks!

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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