What is the sum of the coefficients in the polynomial x^3 + 2x^2 - 9x - 18?

To find the sum of the coefficients in the polynomial (x^3 + 2x^2 - 9x - 18), we can evaluate the polynomial at (x = 1). This approach works because substituting (x = 1) effectively adds all the coefficients together.

Let's compute:

[

P(1) = 1^3 + 2(1^2) - 9(1) - 18

]

Calculating each term:

1. (1^3 = 1)

2. (2(1^2) = 2)

3. (-9(1) = -9)

4. The constant term is (-18)

Now, adding these values together:

[

1 + 2 - 9 - 18

]

This simplifies step-by-step:

[

1 + 2 = 3

]

[

3 - 9 = -6

]

[

-6 - 18 = -24

]

Thus, the sum of the coefficients is (-24). Therefore, the correct answer is (-24), which was not chosen in the original response. This demonstrates