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Using synthetic division, determine the quotient of the expression below.
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Q. Using synthetic division, determine the quotient of the expression below.
- Set up synthetic division: Set up the synthetic division.To use synthetic division, we need to rewrite the divisor as by factoring out a negative sign. We also need to arrange the dividend in descending powers of , filling in any missing terms with coefficients.The correct order of the dividend is .The number we use for synthetic division is the zero of the divisor , which is .
- Perform synthetic division: Perform the synthetic division.We write down the coefficients of the dividend and the zero of the divisor: Bring down the leading coefficient: ---------------- Multiply the leading coefficient by the zero of the divisor and write the result under the next coefficient: ---------------- Add the numbers in the second column: ---------------- Continue this process for the rest of the coefficients: ---------------- Multiply and add for the last column: ----------------
- Write down result: Write down the result of the synthetic division.The numbers at the bottom row give us the coefficients of the quotient, starting from one degree less than the original polynomial:The quotient is , and the remainder is .
- State final answer: State the final answer.The quotient of the division of by is .
