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If g(v)=14v2+33v+32g(v) = 14v^2 + 33v + 32, use synthetic division to find g(3)g(-3).

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Q. If g(v)=14v2+33v+32g(v) = 14v^2 + 33v + 32, use synthetic division to find g(3)g(-3).
  1. Write Coefficients and Divisor: Write down the coefficients of g(v)g(v) and the value we are dividing by, which is 3-3.
  2. Set Up Synthetic Division: Set up the synthetic division: \newline3143332-3 | 14 33 32
  3. Bring Down First Coefficient: Bring down the first coefficient, 1414, to the bottom row.\newline3143332-3 \,|\, 14\, 33\, 32\newline\phantom{space}\,|_____\newline\phantom{space}\,\,\,\,\,\,\,\,\, 1414
  4. Multiply and Write Result: Multiply 3-3 by 1414 and write the result under the second coefficient, 3333.\newline3143332-3 \,|\, 14 \, 33 \, 32\newline\phantom{000}|_____\newline001442\phantom{00}14 \, -42
  5. Add Second Column: Add the numbers in the second column: 33+(42)=933 + (-42) = -9.\newline3143332-3 \,|\, 14 \, 33 \, 32\newline \,|_____\newline 1414 \, 9-9
  6. Multiply and Write Result: Multiply 3-3 by 9-9 and write the result under the third coefficient, 3232.\newline3143332-3 \,|\, 14 \, 33 \, 32\newline\,\,\,\,\,|_____\,\newline\,\,\,\,1414 \,9-9 \, 2727
  7. Add Third Column: Add the numbers in the third column: 32+27=5932 + 27 = 59.\newline3143332-3 | 14\quad 33\quad 32\newline\phantom{space}|\underline{\phantom{space}}\newline\phantom{space}1495914\quad -9\quad 59

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