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Complete the synthetic division problem below: 2| 1 5 −14 ​What is the quotient in polynomial form? A. x+ 5 B. x−7 C. x+ 7 D. x−5
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Answer

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Step 1:
I'll solve this synthetic division problem step by step:

Step 2:
: Identify the divisor and dividend

- The dividend is the polynomial $$1x^{2} + 5x - 14
- The divisor is 2

Step 3:
: Set up synthetic division

- Bring down the first coefficient (1) - Multiply and bring down the next values

Step 4:
: Perform synthetic division

\begin{array}{r}
2 \enclose{longdiv}{1 \quad 5 \quad - 14} \ \underline{2 \quad 14} \ 1 \quad 7 \quad 0 \end{array}

Step 5:
: Interpret the result

- The first row is the original coefficients - The second row shows the multiplications - The bottom row gives the coefficients of the quotient

Step 6:
: Write the quotient polynomial

- The bottom row gives us $$1x + 7
- This simplifies to x + 7

Final Answer

Key Insights: - In synthetic division, we're dividing the polynomial by (x - 2) - The bottom row represents the coefficients of the quotient - The last number (0) would represent the remainder, which is zero in this case