Use synthetic division to find the result when 3x3 + 3x² – 10x – 20 is divided byr(x)X – 2. If there is a remainder, express the result in the form q(x) +6(0)

Given:
An expression:
[tex]3x^3+3x^2-10x-20[/tex]To find:
Use synthetic division to find the result when the expression is divided by x - 2.
Solution:
The synthetic division step by step is shown below:
So, from the above division, we get the quotient 3x^2 + 9x + 8 and the remainder is -4.
Thus, the answer is:
[tex]3x^2+9x+8+\frac{-4}{x-2}[/tex]