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.

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

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