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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 , which are , , and .
- Bring down leading coefficient: Bring down the leading coefficient, which is .
- Multiply root by leading coefficient: Multiply the root, which is , by the leading coefficient, , and write the result, , under the second coefficient, .
- Add second coefficient and result: Add the second coefficient, , and the result from the previous step, , to get . Write this under the line.
- Multiply root by new number: Multiply the root, , by the new number, , and write the result, , under the third coefficient, .
- Add third coefficient and result: Add the third coefficient, , and the result from the previous step, , to get . Write this under the line; this is the remainder.
- Identify quotient and remainder: The numbers on the bottom line are the coefficients of the quotient polynomial , and the last number is the remainder. So, and the remainder is .
- Write final answer in form: Write the final answer in the form . The quotient polynomial is , the remainder is , and the divisor is . So, the final answer is .
