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If , use synthetic division to find .
Full solution
Q. If , use synthetic division to find .
- Write Coefficients and Value: Write down the coefficients of the polynomial and the value we are evaluating, which is .
- Set up Synthetic Division: Set up the synthetic division by placing the value outside the division box and the coefficients , , and inside the box.
- Bring Down Leading Coefficient: Bring down the leading coefficient, which is , to the bottom row.
- Multiply and Write Result: Multiply (the value we are evaluating at) by the number we just brought down () and write the result () under the next coefficient ().
- Add Numbers in Second Column: Add the numbers in the second column () to get and write this number in the bottom row.
- Multiply and Write Result: Multiply by the number we just wrote in the bottom row () and write the result () under the next coefficient ().
- Add Numbers in Third Column: Add the numbers in the third column to get and write this number in the bottom row.
- Find Remainder: The number in the bottom right corner () is the remainder, which represents the value of .
