Final Answer:
When performing synthetic division of P(x) = 2x^3 + 7x^2 - 2x + 9 by (x - 10), the result for P(10) is 1909.
Step-by-step explanation:
To find P(10) using synthetic division, first set up the coefficients of the polynomial function P(x) = 2x^3 + 7x^2 - 2x + 9. Using synthetic division involves setting up a simplified form of long division. Align the coefficients of the polynomial in descending order and perform the division by the factor (x - 10), where 10 is the value for which you want to find P(10).
The coefficients of the polynomial are 2, 7, -2, and 9, representing the coefficients of x^3, x^2, x, and the constant term respectively. Set up the synthetic division bracket, bringing down the first coefficient (2) and performing the division steps by multiplying, adding, and bringing down the next coefficient until completing the process.
Once the synthetic division steps are completed, the remainder will be the value of P(10). In this case, after performing the synthetic division, the remainder obtained is 1909. Therefore, when x is substituted with 10 in the polynomial function P(x), the result is 1909, which represents the value of P(10).