Question

answer 11th question. ​

Answer 1

Long Division Method:

x² + x + 1) x⁴ - 2x³ + 2x² + x + 4(x² - 3x + 4

               x⁴  + x³  +  x²

               -------------------------------

                      -3x³ + x² + x + 4

                     -3x³ - 3x² - 3x

             ---------------------------------

                                4x² + 4x + 4

                                4x² + 4x + 4

                  ------------------------------------

                                                 0

∴ Quotient = x² - 3x + 4, Remainder = 0.

Verification:

Dividend = Divisor * Quotient + Remainder

               = (x² + x + 1) * (x² - 3x + 4) + 0

               = x⁴ - 3x³ + 4x² + x³ - 3x² + 4x + x² - 3x + 4

               = x⁴ - 2x³ + 2x² + x+ 4

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Answer 2

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