Please peform the indicated operation

Question

(6x3 − 32x2 + 30x + 36) ÷ (x2 − 6x + 9)

Answer 1

If we factor the divisor, we get

 

(x - 3)(x - 3)

 

This gives us a root of 3.

 

Divide the coefficients of the cubic factor by 3.

 

 

3 |  6        -32          30           36

 

                 18         -42          -36

____________________________

      6        -14         -12             0

 

 

 

Then divide the coefficients of the quotient by 3 to get your answer.

 

3 |  6         -14           -12

 

                  18            12

________________________

      6           4              0

 

 

The final quotient is then  (6x + 4).

Answer 2

 

P(x)=6x3−32x2+30x+36

Q(x)=x2−6x+9

P(x) divided by Q(x) is:

P(x)Q(x)=6x+4

with the remainder of 0 .

 

                                                        X^2-6X+9

                                                                6X+4      Now Multiply

                                                    __________________

 

                                                     6X^3 -36X^2 +54X 

                                                               +4X^2 -24X    +36

                                              ____________________________

 

                                               = 6X^3 -32X^2 +30X +36         ----->   Checks

 

 
 

Answer 3

(6x³ − 32x² + 30x + 36) ÷ (x² − 6x + 9)

 

                6x - 26

              _____________________

x²-6x+9 /  6x³  - 32x² +  30x +  36      multiply by 6x

              -(6x³  -  6x²   + 54x)             subtract from original

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

                       -26x² - 24x + 36          multiply by -26

                     -(-26x² +156x-234)       subtract

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

                              -180x + 270         remainder

************************************

(6x³ − 32x² + 30x + 36) ÷ (x² − 6x + 9)

 

= 6x - 26 + (-180x+270)/(x² -6x+9)