Answer :
Final answer:
To calculate P(7) using synthetic division, write down the coefficients of P(x) and use 7 for dividing. Carry down the first number, multiply and add to next, repeating this till end. Final value represents P(7).
Explanation:
To calculate P(7) using synthetic division, you should start by setting up your synthetic division tableau. Write down the coefficients of P(x) in descending order of x's powers, i.e., 6, -40, 16, -200, -60, -69, 13, -139. The number to be divided (7 in this case) goes on the left.
Carry down the first number (6) and multiply with 7, placing the product under the second number (-40). Add these two numbers (-40+42=-2) and repeat this process across the row.
The final value in the bottom row represents P(7). In this problem, synthetic division simplifies the calculations greatly compared to directly substituting x=7 into P(x).
Make sure to follow all the steps correctly for an accurate result.
Learn more about Synthetic Division here:
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