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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.