Help with Polynomial Division

[Joebird]

I can't seem to get these 2 problems worked out,

(6x^3 - 16x^2 + 17x - 6) divided by (3x - 2)

and

(3x^3 + 17x^2 + 15x + 2) divided by (x + 5)

Any help is greatly appreciated!

Thanks

 

[kaebun]

have you tried synthetic division? im not sure how'd you do it fo the first but for the second it would be
5| 3 17 15 2
15 160 875
3 32 175 877
so your answer would be 3x^2+32x+175+(877/(x+5))

 

[Unco]

You have the right idea, Kaebun -- just note that if (x+5)=0 --> x=-5.

You could use synthetic division with the first one, too, Joebird, with x=2/3 (from 3x-2=0); which is a root by the remainder test.

Or you could long divide.

            2x^2 
         \------------------------
  3x - 2 |  6x^3 - 16x^2 + 17x - 6 
         /  6x^3 -  4x^2
            ------------
                  -12x^2 + 17x
              
                    etc