Question

Evaluate the function f(x) = 5x^3 + 27x^2 - 13x + 30 at x = -6.

Answer 1

To find the value of the function at x = -6, one must substitute -6 into the polynomial and simplify. The result of the evaluation is f(-6) = 0.

Step-by-step explanation:

The question asks to evaluate the function f(x) = 5x^3 + 27x^2 - 13x + 30 at x = -6. This is a problem of substituting a given value into a polynomial function to find its value.

We proceed by substitution:

1. f(-6) = 5(-6)^3 + 27(-6)^2 - 13(-6) + 30
2. f(-6) = 5(-216) + 27(36) + 78 + 30
3. f(-6) = -1080 + 972 + 78 + 30
4. f(-6) = -1080 + 1080 = 0

So the value of f(x) when x = -6 is 0.