Checking my answer by showing dividend

Question

Hello,

    I'm not sure how to show an answer for the below question. I'm supposed to show my answer by dividend = (divisor)(quotient) + remainder. Any help please.

 

(6x^2 - 5x+2) / (x+1)

Answer 1

It is important to know the definitions:

   The dividend is the number being divided.  The quotient is the whole number given by dividing the dividend by the divisor.  The remainder is the amount left over after the division.

    For example, if 20 is the dividend and 7 is the divisor, the quotient is 2 and the remainder is 6.

 

This problem may be solved by long division or by synthetic division.

 

The dividend is:   (6x^2 -  5x + 2)

The divisor is:   (x + 1)

The quotient is:  (6x - 11)      [see long division below]

The remainder is:  13

 

So,  (6x^2 -  5x + 2) = (x + 1)(6x - 11) + 13

 

To check:

      Is (x+1)(6x-11)  + 13  =  6x^2 - 5x + 2   ?

          (6x^2 -11x + 6x - 11) + 13  =  6x^2 - 5x + 2   ?        [use FOIL]

          6x^2 - 5x + 2   =  6x^2 - 5x + 2   ?       yes.

 

Long division:

 

                    6x     -11

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

(x+1)    )  6x^2    -5x   +2

                6x^2   + 6x

                            ----------

                            -11x + 2

                            -11x - 11

                            -----------

                                       13

Answer 2

6x + 1 + 1/(x + 1)