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How do you divide #(x^4 + 81) ÷ (x + 3)#?

Answer 1

Chloe Alexander

#x^3-3x^2+9x-27+162/(x+3)#

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Answer 2

Benjamin Achtenberg

To divide the polynomial ( (x^4 + 81) ) by ( (x + 3) ), you can use polynomial long division or synthetic division. Here's the result using polynomial long division:

                x^3 - 3x^2 + 9x - 27
          ___________________________
x + 3  |  x^4 + 0x^3 + 0x^2 + 0x + 81
                - (x^4 + 3x^3)
                _______________
                        - 3x^3
                        - (-3x^3 - 9x^2)
                        _______________
                                   - 9x^2
                                   - (-9x^2 - 27x)
                                   _______________
                                             27x
                                             - (27x + 81)
                                             ____________
                                                      81

So, ( (x^4 + 81) \div (x + 3) = x^3 - 3x^2 + 9x - 27 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.