Question

evaluate the function for the given value of x.\
g(x) = -x³ + 3x² + 5x + 1 ; x = -12\
g(-12) = \square

Explanation:

Step1: Substitute \( x = -12 \) into \( g(x) \)

Substitute \( x = -12 \) into \( g(x) = -x^3 + 3x^2 + 5x + 1 \), we get:
\( g(-12) = -(-12)^3 + 3(-12)^2 + 5(-12) + 1 \)

Step2: Calculate each term

• Calculate \( -(-12)^3 \): \( (-12)^3 = -1728 \), so \( -(-12)^3 = 1728 \)
• Calculate \( 3(-12)^2 \): \( (-12)^2 = 144 \), so \( 3(-12)^2 = 3\times144 = 432 \)
• Calculate \( 5(-12) \): \( 5\times(-12) = -60 \)

Step3: Sum up all terms

Sum the results: \( 1728 + 432 - 60 + 1 \)
First, \( 1728 + 432 = 2160 \)
Then, \( 2160 - 60 = 2100 \)
Finally, \( 2100 + 1 = 2101 \)

Answer:

\( 2101 \)