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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 of the polynomial as , , and .
- Bring down leading coefficient: Bring down the leading coefficient () to the bottom row.
- Multiply root by number: Multiply the root () by the number just brought down () and write the result () under the next coefficient ().
- Add numbers in column: Add the numbers in the second column and write the result in the bottom row.
- Multiply root by new number: Multiply the root () by the new number in the bottom row () and write the result () under the next coefficient ().
- Add numbers in column: Add the numbers in the third column and write the result in the bottom row.
- Identify quotient and remainder: The numbers in the bottom row represent the coefficients of the quotient polynomial and the remainder . The quotient polynomial is and the remainder is .
- Write final answer: Write the final answer in the form . Since the remainder is , the division is exact and the result is just the quotient polynomial .
