Use synthetic division to solve (2x^34x^2-35x15)/(x-3). what is the quotient?

quotient is 2x^2 + 10x - 5

Solution:

The first polynomial is miswritten.

The right one is: 2x^3 + 4x^2 - 35x + 15.

So, the division is [2x^3 + 4x^2 - 35x + 15] / (x - 3)

The synthetic division uses the coeffcients and obviate the letters, but you have to be sure to respect the place of the coefficient.

So, in this case it is:

3 | 2      4    -35    15
  
    2     10     - 5      0

So, the quotient is 2x^2 + 10x - 5, and the remainder is 0.

I like to show it in this other way:

   | 2     4     -35     15
   |
   |
3 |       +6    +30     -15
 
    2     10    - 5         0

Of course they are the same coefficients and the answer continue being quotien 2x^2 + 10x - 5, remainder 0.