use synthetic substitution to find the value of the given polynomial function at the indicated value.

a. P(x)=x^4+x^3-4x^2-8x; P(-1)

If you mean synthetic division, the web site below shows all the details involved.

http://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php

thanks again... :)

To evaluate the polynomial function P(x) = x^4 + x^3 - 4x^2 - 8x at the indicated value (-1) using synthetic substitution, follow these steps:

Step 1: Write down the coefficients of the polynomial in descending order of exponents. In this case, the polynomial is P(x) = x^4 + x^3 - 4x^2 - 8x, so the coefficients are 1, 1, -4, -8.

Step 2: Set up the synthetic substitution table. The leftmost column should include the coefficients of the polynomial, and the rightmost column should include the value you want to substitute (-1).

| 1 | 1 | -4 | -8
-1 | |

Step 3: Copy the first coefficient (1) to the bottom row below the horizontal line.

| 1 | 1 | -4 | -8
-1 | |

Step 4: Multiply the value in the bottom row (-1) with the copied coefficient (1), and write the result beneath the second coefficient.

| 1 | 1 | -4 | -8
-1 | -1 |

Step 5: Add the result to the corresponding coefficient in the previous row.

| 1 | 1 | -4 | -8
-1 | -1 | 0 |

Step 6: Repeat steps 4 and 5 until you reach the last coefficient.

| 1 | 1 | -4 | -8
-1 | -1 | 0 | 4
-1 | 1 | -1 | 3

Step 7: The last number in the bottom row is the value of the polynomial function at the indicated value. In this case, P(-1) = 3.

Therefore, when you substitute x = -1 into the polynomial function P(x) = x^4 + x^3 - 4x^2 - 8x, the result is 3.