How do you factor # z^4 - 12z^2 + 27#?

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Answer 1 · 2015-05-02T03:13:17

The answer is #(z+3)(z-3)(z^2-3)# .

Factor #z^4-12z^2+27# .

Find two numbers that when added together make #-12#, and when multiplied together make #27#. The numbers #-3# and #-9# these conditions.

#z^4-12z^2+27=(z^2-3)(z^2-9)#

#(z^2-9)# is an example of the difference of squares and can be factored further.

#(z^2-9)=(z+3)(z-3)#

Combine.

#(z+3)(z-3)(z^2-3)#