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If g(u)=22u2+33u+27g(u) = 22u^2 + 33u + 27, use synthetic division to find g(1)g(-1).

Full solution

Q. If g(u)=22u2+33u+27g(u) = 22u^2 + 33u + 27, use synthetic division to find g(1)g(-1).
  1. Write Coefficients and Value: To use synthetic division, we first write down the coefficients of g(u)g(u): 2222, 3333, and 2727. Then we write 1-1 to the left since that's the value we're evaluating for.
  2. Bring Down First Coefficient: Bring down the first coefficient, 2222, as is.
  3. Multiply and Write Result: Multiply 1-1 by 2222 and write the result, 22-22, under the second coefficient, 3333.
  4. Add Coefficient and Number: Add the second coefficient, 3333, and the number below it, 22-22, to get 1111. Write this below the line.
  5. Multiply and Write Result: Multiply 1-1 by the new number, 1111, and write the result, 11-11, under the third coefficient, 2727.
  6. Add for Remainder: Add the third coefficient, 2727, and the number below it, 11-11, to get 1616. Write this below the line; this is the remainder and also the value of g(1)g(-1).

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