SOLUTION: factor completely x^6 - 14x^4 + 49x^2 i have no clue where to even begin please help

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Question 580002: factor completely
x^6 - 14x^4 + 49x^2
i have no clue where to even begin please help
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can factor out an +x%5E2+
+x%5E2%2A%28+x%5E4+-+14x%5E2+%2B+49+%29+
Now I can make the substitution +x%5E2+=+z+
+z%2A%28+z%5E2+-+14z+%2B+49+%29+
To factor this completely, I
complete the square on the 2nd factor:
+z%5E2+-+14z+%2B+%2814%2F2%29%5E2+=+-49+%2B+%2814%2F2%29%5E2+
+z%5E2+-+14z+%2B+49+=+-49+%2B+49+
+%28+z+-+7+%29%5E2+=+0+
+z+-+7+=+0+
This is called a double root, so the factorization is:
+z%2A%28+z+-+7+%29%5E2+
Now substitute +z+=+x%5E2+
+x%5E2%2A%28+x%5E2+-+7+%29%5E2+
This can be factored 1 more step:
+x%5E2%2A%28+x+%2B+sqrt%287%29+%29%5E2%28+x+-+sqrt%287%29+%29%5E2+
Hope I got it
Here's a plot of the equation:
+graph%28+500%2C+500%2C+-4%2C+4%2C+-2%2C+16%2C+x%5E6+-+14x%5E4+%2B+49x%5E2+%29+