Use synthetic division to solve (2x3+4x2-35x+15) divided by (x-3) what is the quotient?

There is a nice shortcut for long division of polynomials when dividing by  divisors of the form . We name this shortcut as synthetic division.

To divide we use the pattern  for synthetic division of a cubic polynomial summarized in Figure 1. You should set up the arrays as indicated in Figure 2.Then use the synthetic division pattern by adding terms  in columns and multiplying the results by 3 as illustrated in Figure 3.

Finally, the quotient is: