QQuestionMathematics
QuestionMathematics
Complete the synthetic division problem below:
−3∣ 1 2 −2 3
What is the quotient in polynomial form?
A. x^2 − x+ 3
B. x^2 − x+ 1
C. x^2 + x−1
D. x^2 + x−3
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Answer
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Step 1:I'll solve this synthetic division problem step by step:
Step 2:: Set up the synthetic division
- The divisor is $$-3
- The dividend is 1x^{2} + 2x - 2 + 3
Step 3:: Perform synthetic division
\begin{array}{r}
- Multiply 1 by - 3 and add to the next coefficient - 3 \overline{)1 \quad 2 \quad - 2 \quad 3} \ \quad \quad 1 \quad - 3 \quad 3 \quad - 3 \ \quad \quad 1 \quad - 1 \quad 1 \quad 0 \end{array}
Step 4:: Interpret the results
- The last number ($$0$$) is the remainder
- The bottom row represents the coefficients of the quotient polynomial
Step 5:: Write the quotient polynomial
- The coefficients are $$1, -1, 1
- This means the quotient is x^{2} - x + 1
Final Answer
Note: In synthetic division, the coefficients of the quotient are found by the bottom row of the division process, and the last number represents the remainder.
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