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Sydnee Potter
Mathematics
7 June, 02:21
Determine the linear factors for x4-2x^2+1
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Mckenzie Browning
7 June, 02:29
0
Didn't you mean x^4-2x^2+1?
Choose "p" to represent x^2. Then p^2 - 2p + 1 = (p-1) (p-1)
These results are equivalent to (x^2-1) (x^2+1).
x^2-1 can be factored: (x-1) (x+1)
x^2-1 (again) can be factored: (x-1) (x+1)
Then the factored expression is (x-1) ^2 * (x+1) ^2.
Check this by multiplication. Do you obtain x^4 - 2x^2 + 1?
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Dashawn Benjamin
7 June, 02:30
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Use a substitution: let b = x^2
Then b^2 = x^4.
Now you need to factor
b^2 - 2b + 1 =
(b - 1) ^2
Since b = x^2, now we replace b with x^2 and factor again.
(x^2 - 1) ^2 is the square of a difference of squares.
= (x^2 - 1) (x^2 - 1)
= (x + 1) (x - 1) (x + 1) (x - 1)
= (x + 1) ^2 (x - 1) ^2
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