Use synthetic division to find (x^2 - 9x + 14) ÷ (x - 2). Write your answer in the form q(x) + r/d(x), where q(x) is a polynomial, r is an integer, and d(x) is a linear polynomial. Simplify any fractions. ______

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Use synthetic division to find (x^2 - 9x + 14) ÷ (x - 2).  Write your answer in the form q(x) + r/d(x), where q(x) is a polynomial, r is an integer, and d(x) is a linear polynomial. Simplify any fractions. ______

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Set up synthetic division: Set up synthetic division with 2 as the root from (x - 2) and the coefficients of the polynomial x^2 - 9x + 14 as 1, -9, and 14.Bring down leading coefficient: Bring down the leading coefficient (1) to the bottom row.Multiply root by number: Multiply the root (2) by the number just brought down (1) and write the result (2) under the next coefficient (-9).Add numbers in column: Add the numbers in the second column (-9 + 2 = -7) and write the result (-7) in the bottom row.Multiply root by new number: Multiply the root (2) by the new number in the bottom row (-7) and write the result (-14) under the next coefficient (14).Add numbers in column: Add the numbers in the third column (14 + (-14) = 0) and write the result (0) in the bottom row.Identify quotient and remainder: The numbers in the bottom row represent the coefficients of the quotient polynomial q(x) and the remainder r. The quotient polynomial is x - 7 and the remainder is 0.Write final answer: Write the final answer in the form q(x) + r/d(x). Since the remainder is 0, the division is exact and the result is just the quotient polynomial q(x).

Use synthetic division to find $(x^2 - 9x + 14) \div (x - 2)$ . $\newline$ Write your answer in the form $q(x) + \frac{r}{d(x)}$ , where $q(x)$ is a polynomial, $r$ is an integer, and $d(x)$ is a linear polynomial. Simplify any fractions. $\newline$ _________

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