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If g(t)=8t2+15t33g(t) = 8t^2 + 15t - 33, use synthetic division to find g(3)g(-3).

Full solution

Q. If g(t)=8t2+15t33g(t) = 8t^2 + 15t - 33, use synthetic division to find g(3)g(-3).
  1. Write Coefficients and Value: First, we write down the coefficients of g(t)g(t) which are 88, 1515, and 33-33, and the value we are evaluating, which is 3-3.
  2. Set up Synthetic Division: Set up the synthetic division: \newline3-3 | 88 1515 33-33\newline | 24-24 2727\newline ----------------\newline 88 9-9 6-6
  3. Bring Down Leading Coefficient: Bring down the leading coefficient to the bottom row.\newline3-3 | 88 1515 33-33\newline | 24-24 2727\newline ----------------\newline 88 9-9 6-6
  4. Multiply and Add: Multiply 3-3 by 88 and add the result to 1515, then write the result below the 1515.\newline3    8  15  33-3 \;|\; 8 \; 15 \; -33\newline                    24  27\;\;\;|\;\;\;\;\;\;\; -24 \; 27\newline----------------\newline      8  9  6\;\;\; 8 \; -9 \; -6
  5. Calculate g(3)g(-3): Multiply 3-3 by 9-9 and add the result to 33-33, then write the result below the 33-33.
    3-3 | 88 1515 33-33
    | 24-24 3-300
    ----------------
    88 9-9 3-333
  6. {

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