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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 by using the root of the divisor , which is .
- Write coefficients of dividend: Write down the coefficients of the dividend , which are , , and .
- Bring down leading coefficient: Bring down the leading coefficient, which is .
- Multiply by : Multiply by the number just written below the line, which is , and write the result, , in the next column under .
- Add numbers in second column: Add the numbers in the second column, , to get . Write this below the line.
- Multiply by again: Multiply by the new number just written below the line, which is , and write the result, , in the next column under .
- Add numbers in third column: Add the numbers in the third column, , to get . Write this below the line.
- Identify quotient and remainder: The numbers below the line represent the coefficients of the quotient polynomial and the remainder. So, the quotient is and the remainder is .
- Write final answer: Write the final answer in the form , where is , is , and is .
