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

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

• A. -24
• B. 0
• C. 2
• D. -20

Answer: (D)

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

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