Question

using long division method show that the polynomial p(x)=x3+1 is divisible by q(x)=x+1. verify your result using factor theorem

Answer 1

Long division

        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

Answer 2

Answer:

Step-by-step explanation: