Answer:
p(-1) = -3.
Step-by-step explanation:
To find p(-1) using synthetic division, we'll substitute -1 into the polynomial p(z) and perform the synthetic division. Let's do it step by step:
1. Write down the coefficients of the polynomial in descending order: 15, -24, -35, 1.
2. Set up the synthetic division table, with -1 written on the left side.
3. Bring down the first coefficient, which is 15.
4. Multiply -1 by 15, which gives -15. Write the result below the next coefficient.
5. Add the two numbers in the second column: -24 + (-15) = -39. Write the result below the line.
6. Multiply -1 by -39, which gives 39. Write the result below the next coefficient.
7. Add the two numbers in the third column: -35 + 39 = 4. Write the result below the line.
8. Multiply -1 by 4, which gives -4. Write the result below the next coefficient.
9. Add the two numbers in the fourth column: 1 + (-4) = -3. Write the result below the line.
The result of the synthetic division is -3. Therefore, p(-1) = -3.
