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

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

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Answer 1 · 2015-05-02T03:13:17

The answer is $(z + 3) (z - 3) (z^{2} - 3)$ $(z+3)(z-3)(z^2-3)$ .

Factor $z^{4} - 12 z^{2} + 27$ $z^4-12z^2+27$ .

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

$z^{4} - 12 z^{2} + 27 = (z^{2} - 3) (z^{2} - 9)$ $z^4-12z^2+27=(z^2-3)(z^2-9)$

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

$(z^{2} - 9) = (z + 3) (z - 3)$ $(z^2-9)=(z+3)(z-3)$

Combine.

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

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

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