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If , use synthetic division to find .
Full solution
Q. If , use synthetic division to find .
- Set up synthetic division: First, set up the synthetic division with as the root we're testing and the coefficients of in descending order of .
- Bring down first coefficient: The synthetic division setup looks like this:Now, bring down the to the bottom row.
- Multiply and write result: Multiply by and write the result under the next coefficient:\,\,|\,\underline{\quad\quad\quad\quad}\,\,|\, \,\,
- Add numbers in second column: Add the numbers in the second column:Write this sum in the bottom row. |_______ |
- Multiply and write result: Multiply by and write the result under the next coefficient:\phantom{1 \,|\,}_______19
- Add numbers in third column: Add the numbers in the third column:Write this sum in the bottom row. |_______ |
- Find remainder: The number in the bottom right is the remainder, which represents .
