Q. If p(v)=6v2−22v−39, use synthetic division to find p(3).
Write Coefficients and Value: Write down the coefficients of the polynomial and the value we are evaluating, which is 3.
Set up Synthetic Division: Set up the synthetic division by placing the value 3 outside the division box and the coefficients 6, −22, and −39 inside the box.
Bring Down Leading Coefficient: Bring down the leading coefficient, which is 6, to the bottom row.
Multiply and Write Result: Multiply 3 (the value we are evaluating at) by the number we just brought down (6) and write the result (18) under the next coefficient (−22).
Add Numbers in Second Column: Add the numbers in the second column (−22+18) to get −4 and write this number in the bottom row.
Multiply and Write Result: Multiply 3 by the number we just wrote in the bottom row (−4) and write the result (12) under the next coefficient (−39).
Add Numbers in Third Column: Add the numbers in the third column (−39+12) to get −27 and write this number in the bottom row.
Find Remainder: The number in the bottom right corner (−27) is the remainder, which represents the value of p(3).
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