Final answer:
To solve the given expression x^(3) + 6x^(2) - 11x - 66, we can use synthetic division or factoring. Applying synthetic division, we find the factors or roots of the expression to be x = -√66 and x = √66.
Step-by-step explanation:
The given expression is:
x^(3) + 6x^(2) - 11x - 66
To solve this expression, we need to use the methods of factoring or synthetic division to find the roots or factors of the expression.
Let's start by applying synthetic division. The first step is to set up the synthetic division table:
x | 1 6 -11 -66
Next, we divide the first term of the expression by x.
We then multiply the divisor by -66 and write the result underneath the next term.
Add the results:
x | 1 6 -11 -66
-66 0 66 -0
x^(2) + 0x - 66 = x^(2) - 66
We can then factor x^(2) - 66 to further simplify the expression and solve for the roots.
Factoring the expression, we get:
(x + √66)(x - √66)
Therefore, the factors or roots of the given expression are x = -√66 and x = √66.