How do you factor #x^ { 4} - 5x ^ { 2} + 4#?

1 Answer
George C.
Dec 7, 2016

#x^4-5x^2+4 = (x-2)(x+2)(x-1)(x+1)#

Explanation:

Treat this first as a quadratic in #x^2#, then use the difference of squares identity to reduce it further to linear factors.

The difference of squares identitty can be written:

#a^2-b^2 = (a-b)(a+b)#

So we find:

#x^4-5x^2+4 = (x^2)^2-5(x^2)+4#

#color(white)(x^4-5x^2+4) = (x^2-4)(x^2-1)#

#color(white)(x^4-5x^2+4) = (x^2-2^2)(x^2-1^2)#

#color(white)(x^4-5x^2+4) = (x-2)(x+2)(x-1)(x+1)#

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