Question

Using long division method, show that (1 + x) is a factor of the polynomial
(- 1 + x4)

answer me fast please​

Answer 1

x^2 - x + 1

       ____________

x+1  [ x^3             + 1

       [ x^3 + x^2

         ----------------

                  -x^2         + 1

                  -x^2 - x

                  ------------

                          x   + 1

                          x  +   1

                          ----------

                             0  

so, the answer is:

x² - x + 1

Using factor theorm:

a³ + b³ = (a + b)(a² – ab + b²)

So, x³ + 1 = x³ + 1³ = (x+1)(x² - 2x + 1)

and (x³ + 1) / (x+ 1) = (x+1)(x² - 2x + 1) / (x + 1)

The (x + 1) brackets cancel out and we are left with

x² - 2x + 1