Factor Theorem

Question

Use the Factor Theorem to determine if the first polynomial is a factor of the second polynomial. I have to show work.

4.

Is (x - 3) a factor of 2x3 - 11x2 + 12x + 9?     

Answer 1

Just use synthetic division (put "3" in the notch):   

 

3|  2  -11  12    9

          6    -15  -9

     2   -5   -3    0

 

Since synthetic division (for ÷ by (x-3) yields the above remainder 0, (x-3) is indeed a factor of the cubic polynomial.