How do you factor completely $x^{4} - 24 x^{2} - 25$ $x^4-24x^2-25$ ?

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How do you factor completely $x^{4} - 24 x^{2} - 25$ $x^4-24x^2-25$ ?

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Answer 1 · 2016-04-16T21:20:37

$x^{4} - 24 x^{2} - 25 = (x - 5) (x + 5) (x^{2} + 1)$ $x^4-24x^2-25=(x-5)(x+5)(x^2+1)$

Explanation:

$x^{4} - 24 x^{2} - 25 = (x^{2} - 25) (x^{2} + 1)$ $x^4-24x^2-25=(x^2-25)(x^2+1)$
$(x^{2} - 25) = (x^{2} - 5^{2}) = (x - 5) (x + 5)$ $(x^2-25)=(x^2-5^2)=(x-5)(x+5)$
$x^{4} - 24 x^{2} - 25 = (x - 5) (x + 5) (x^{2} + 1)$ $x^4-24x^2-25=(x-5)(x+5)(x^2+1)$

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How do you factor completely $x^{4} - 24 x^{2} - 25$ $x^4-24x^2-25$ ?

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How do you factor completely $x^{4} - 24 x^{2} - 25$ $x^4-24x^2-25$ ?