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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 the root of the divisor, which is , and the coefficients of the dividend, which are , , and .
- Bring down leading coefficient: Bring down the leading coefficient, which is .
- Multiply root by coefficient: Multiply the root by the leading coefficient we just brought down, which is , and write this number under the second coefficient, .
- Add numbers in second column: Add the numbers in the second column, , and write this number below the line.
- Multiply root by new number: Multiply the root by the new number we just got, which is , and write this number under the third coefficient, .
- Add numbers in third column: Add the numbers in the third column, , and write this number below the line.
- Write result of synthetic division: Write the result of synthetic division in the form , where is the quotient polynomial and is the remainder. The coefficients from the synthetic division give us and the remainder is .
