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Please peform the indicated operation

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

Comments

I got an incorrect answer for this problem. I tried another one similar to th problem and got an anwswer hat was 7x+3, the practice versions answers are very similar to the quiz version answer.
so I'm confused on how to to work tis prolem out.
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3 Answers

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).

 

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
 


 
 

Comments

Try Synthetic Division.,.sometimes helps
(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)