What is the completely factored form of x4 8x2 9

Asked by maham237 @ 28/05/2021 in Mathematics viewed by 438 People

factored form of x4 8x2 – 9

Answered by maham237 @ 28/05/2021

For this case we have the following polynomial:

$x ^ 4 + 8x ^ 2 - 9$

We make the following change of variables:

$u = x ^ 2$

Rewriting we have

$u ^ 2 + 8u - 9$

Factoring the second order polynomial we have:

$(u + 9) (u-1)$

Then, returning the change we have:

$(x ^ 2 + 9) (x ^ 2-1)$

Finally, we factor the expression in the parentheses of the second term:

$(x ^ 2 + 9) (x + 1) (x-1)$

Answer:

the completely factored form is:

$(x ^ 2 + 9) (x + 1) (x-1)$

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