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Answer :
To calculate P(7) for the polynomial P(x), synthetic division requires writing out the coefficients and systematically adding and multiplying by 7. Direct substitution simply involves replacing x with 7 in the polynomial and calculating the result according to the order of operations.
To calculate P(7) using synthetic division, we will follow these steps:
Write down the coefficients of P(x): 5, -34, 10, -109, -60, -69, 12, -125.
Place the number 7 outside the division symbol.
Bring down the first coefficient (5) and multiply it by 7, placing the result under the second coefficient (-34).
Add down the column and continue this process of multiplying by 7 and adding down the column until the last number is reached.
The final number is the value of P(7).
To calculate P(7) by direct substitution:
Substitute x with 7 in the polynomial P(x).
Follow the order of operations to evaluate the expression, starting with raising 7 to the appropriate powers and then applying multiplication, subtraction, and addition.
The final result will yield the value of P(7).
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