Answer:
p(-4) = -8425
Step-by-step explanation:
Here's how you find p(-4) using synthetic division:
1. Write down the coefficients of the polynomial in descending order: 92, -162, -17, -13.
2. Set up the synthetic division table, with -4 written on the left side.
3. Bring down the first coefficient, which is 92.
4. Multiply -4 by 92, which gives -368. Write the result below the next coefficient.
5. Add the two numbers in the second column: -162 + (-368) = -530. Write the result below the line.
6. Multiply -4 by -530, which gives 2120. Write the result below the next coefficient.
7. Add the two numbers in the third column: -17 + 2120 = 2103. Write the result below the line.
8. Multiply -4 by 2103, which gives -8412. Write the result below the next coefficient.
9. Add the two numbers in the fourth column: -13 + (-8412) = -8425. Write the result below the line.
The result of the synthetic division is -8425. Therefore, p(-4) = -8425.
