Question

=

. Consider the polynomial function p given by p(x) = 5x3 + 8x2 – 3x + 1. Evaluate the
function at x = -2.

Answer 1

To evaluate the polynomial function p(x) = 5x^3 + 8x^2 - 3x + 1 at x = -2, one substitutes the value of x into the function and then sums up the results of each term, leading to a final value of -1. The value of the polynomial function p at x = -2 is −1.

Step-by-step explanation:

The student's question involves evaluating the polynomial function p(x) = 5x3 + 8x2 − 3x + 1 at x = -2. To solve this, we substitute x with -2 and calculate the result.

Here is the step-by-step calculation:

1. First, calculate the cubic term: 5(−2)3 = 5(−8) = −40.
2. Next, calculate the quadratic term: 8(−2)2 = 8(4) = 32.
3. Then, calculate the linear term: (−3)(−2) = 6.
4. Finally, add the constant term: 1.
5. Add all the terms together: (−40) + 32 + 6 + 1 = −1.

Thus, the value of the polynomial function p at x = -2 is −1.