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Given that [tex]

x^5 - 2x^4 + 2x^3 - 4x^2 - 3x + 6[/tex] is exactly divisible by [tex]x^2 + 3[/tex], find the remaining real factors of the polynomial.

__________________

I could easily do that question using a calculator, just by graphing it and finding the roots. Another thing i can do is multiply the factor by the general cubic equation, expand the brackets, and then compare the coefficients. But then that leaves me with the polynomial in terms of the product of only 2 of its factors.

If i was given a question like this in a test, how can i show working? How can i do it without even touching a calulator?

Thanks,

Dan.

x^5 - 2x^4 + 2x^3 - 4x^2 - 3x + 6[/tex] is exactly divisible by [tex]x^2 + 3[/tex], find the remaining real factors of the polynomial.

__________________

I could easily do that question using a calculator, just by graphing it and finding the roots. Another thing i can do is multiply the factor by the general cubic equation, expand the brackets, and then compare the coefficients. But then that leaves me with the polynomial in terms of the product of only 2 of its factors.

If i was given a question like this in a test, how can i show working? How can i do it without even touching a calulator?

Thanks,

Dan.

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