Q. If g(z)=z2−7z−24, use synthetic division to find g(4).
Write Coefficients and Divisor: To use synthetic division, we first write down the coefficients of the polynomial g(z)=z2−7z−24, which are 1, −7, and −24. Then we write the number we are dividing by, which is 4, to the left.
Bring Down First Coefficient: We bring down the first coefficient, which is 1, and write it below the line.
Multiply and Write Result: Multiply the number we brought down (1) by 4 and write the result (4) under the next coefficient (−7).
Add Second Column: Add the numbers in the second column (−7+4) to get −3 and write this number below the line.
Multiply and Write Result: Multiply the number we just wrote (−3) by 4 and write the result (−12) under the next coefficient (−24).
Add Third Column: Add the numbers in the third column (−24+−12) to get −36 and write this number below the line.
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