Factoring: All Techniques Combined

Factor each expression.

4) [tex] x^{6} + 2x^{4} - 16x^{2} - 32 [/tex]

x 6 + 2 x 4 − 16 x 2 − 32 = x 4 ( x 2 + 2 ) − 16 ( x 2 + 2 ) = ( x 2 + 2 ) ( x 4 − 16 ) = = ( x 2 + 2 ) ( x 4 − 4 2 ) = ( x 2 + 2 ) ( x 2 − 4 ) ( x 2 + 4 ) = = ( x 2 + 2 ) ( x 2 + 4 ) ( x + 2 ) ( x − 2 ) a 2 − b 2 = ( a − b ) ( a + b )

Answered by Anonymous | 2024-06-10

The expression x 6 + 2 x 4 − 16 x 2 − 32 can be factored to ( x 2 + 2 ) ( x − 2 ) ( x + 2 ) ( x 2 + 4 ) . We used grouping and the difference of squares to simplify the expression step-by-step. The final factored form includes quadratic and linear factors.
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Answered by Anonymous | 2025-04-11