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If g(z)=z27z24g(z) = z^2 - 7z - 24, use synthetic division to find g(4)g(4).

Full solution

Q. If g(z)=z27z24g(z) = z^2 - 7z - 24, use synthetic division to find g(4)g(4).
  1. Write Coefficients and Divisor: To use synthetic division, we first write down the coefficients of the polynomial g(z)=z27z24g(z) = z^2 - 7z - 24, which are 11, 7-7, and 24-24. Then we write the number we are dividing by, which is 44, to the left.
  2. Bring Down First Coefficient: We bring down the first coefficient, which is 11, and write it below the line.
  3. Multiply and Write Result: Multiply the number we brought down (11) by 44 and write the result (44) under the next coefficient (7-7).
  4. Add Second Column: Add the numbers in the second column (7+4)(-7 + 4) to get 3-3 and write this number below the line.
  5. Multiply and Write Result: Multiply the number we just wrote (3)(-3) by 44 and write the result (12)(-12) under the next coefficient (24)(-24).
  6. Add Third Column: Add the numbers in the third column (24+12-24 + -12) to get 36-36 and write this number below the line.

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