How do you fractorise <span title="f(x)=3x^(4)+7x^(3)+x^(2)-7x-4.">f(x)=3x^(4)+7x^(3)+x^(2)-...</span> It has common factor of (x^2-1)?

Question

Please show workings.

Answer 1

Divide the x²-1 into f(x). You will get 3x²+7x+4 which factors into (3x+4)(x+1) so your final total factorization would be

(3x+4)(x+1)(x+1)x-1)

to divide the x²-1 into f(x) you can do it with long division or synthetic division on the factors of x²-1. The long division method would look like this:

            3x²+7x+4

......   ______________

x²-1 │3x^4 +7x^3+x²-7x-4

........  3x^4......... -3x²

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.................7x^3+4x²-7x-4

.................7x^3......-7x

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.........................4x²-4                  

.........................4x²-4

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