Divide the following expression using long division.

Question

(x^{3} + x^{2} + x - 3) ÷ (x - 1)

Answer 1

The trick is to keep track of your signs. I find it useful to put parentheses around the part we subtract in order to distribute the negative sign to each part individually. You might find it easier to distribute the minus sign beforehand; it's up to you.

 

         x² + 2x + 3

        -------------------

x-1 | x³ + x² + x - 3

      -(x³ - x²)

      ----------------

              2x² + x

           -(2x² - 2x)

           -----------------

                     3x - 3

                   -(3x - 3)

                   -----------

                              0

Answer 2

 

x³+x²+x-3

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

    x - 1

 

             2x²+x-3 

= x² +   ----------

                x - 1

 

                     

                     3x - 3                      

 = x² + 2x +  ---------

                      x - 1

 

 = x² + 2x + 3   (with no remainder)