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Use synthetic division to find .Write your answer in the form , where is a polynomial, is an integer, and is a linear polynomial. Simplify any fractions._________
Full solution
Q. Use synthetic division to find .Write your answer in the form , where is a polynomial, is an integer, and is a linear polynomial. Simplify any fractions._________
- Set up synthetic division: Set up synthetic division with as the root from and the coefficients from which are , , and .
- Bring down first coefficient: Bring down the first coefficient, , to the bottom row.
- Multiply and write result: Multiply by and write the result, , under the second coefficient, .
- Add and write result: Add and to get . Write this number under the line in the second column.
- Multiply and write result: Multiply by and write the result, , under the third coefficient, .
- Add and write result: Add and to get . Write this number under the line in the third column. This is the remainder.
- Identify quotient polynomial: The numbers on the bottom row are the coefficients of the quotient polynomial . So, .
- Final answer without remainder: Since the remainder is , the final answer is just without any remainder term.
