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x4-7x2-144

 Oct 21, 2016
 #1
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Factor the following:
x^4-7 x^2-144

x^4-7 x^2-144 = (x^2)^2-7 x^2-144:
(x^2)^2-7 x^2-144

The factors of -144 that sum to -7 are 9 and -16. So, (x^2)^2-7 x^2-144 = (x^2+9) (x^2-16):
(x^2+9) (x^2-16)

x^2-16 = x^2-4^2:
(x^2+9) (x^2-4^2)

Factor the difference of two squares. x^2-4^2 = (x-4) (x+4):
Answer: |(x-4)  (x+4)  (x^2+9)

 Oct 21, 2016

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