Assuming one factor of x^4 - a^4 is x-a (the divisor), what is the other factor?Find the other factor by polynomial division. 

Asked on by vshielder

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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We know that `(x^2-a^2) ` = (x-a)(x+a)



=` (x^2-a^2)(x^2+a^2)`

= `(x-a)(x+a)(x^2+a^2)`


Since (x-a) is a factor of` (x^4-a^4)` , `(x^4-a^4)` is divisible by (x-a).



= `(x-a)(x+a)(x^2+a^2)/(x-a) `

= `(x+a)(x^2+a^2)/(x-a)`


So there are two other factors according to the answer.

They are (x+a) and `(x^2+a^2)` .

If `(x^2+a^2)` is a factor then `x^2 = -a^2 `

So x has no real answers if `(x^2+a^2)` is a factor. So we have to omit it.

So the other factor is (x+a).


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