How do you factor completely #x^4 - 3x^2 - 10#?

1 Answer
Nghi N.
May 5, 2016

#(x^2 + 2)(x + sqrt5)(x - sqrt5)#

Explanation:

#y = x^4 - 3x^2 - 10#.
Call x^2 = X. Factor the quadratic trinomial:
#x^2 - 3x - 10.#
Find 2 numbers knowing sum (b = -3) and product (c = -10). They are the factor pair: (2, -5).
#y = (X + 2)(X - 5) = (x^2 + 2)(x^2 - 5) = (x^2 + 2)(x - sqrt5)(x + sqrt5)#

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