How do you factor #8x ^ { 8} - 48x ^ { 7} + 16x ^ { 6}#?

1 Answer
Vinícius Ferraz
Jul 20, 2017

#8x^6 (x - 3 - sqrt 7)(x - 3 + sqrt 7)#

Explanation:

#x^6 (8x^2 - 48x + 16)#

#= 8x^6 (x^2 - 6x + 2)#

#= 8x^6 (x - x_1)(x - x_2)# // two roots of #x^2 - 6x + 2 = 0#

#Delta = 36 - 4 * 2 = 28#

#x = (6 ± sqrt 28)/2 = 3 ± sqrt 7#

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