There is a nice shortcut for long division of polynomials when dividing by divisors of the form \(x-k\). We name this shortcut as synthetic division.
- To divide \(ax^3+bx^2+cx+d \ by \ x-k\) 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:
\(\boxed{2x^2+10x-5}\)
