Problem

Find the quotient using long division.
\[
\frac{2 x^{3}+3 x^{2}-17 x+2}{x-2}
\]

Answer

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Answer

Final Answer: The quotient of the long division is \(\boxed{2x^2 + 7x - 3}\).

Steps

Step 1 :We are asked to find the quotient of the polynomial long division \(\frac{2 x^{3}+3 x^{2}-17 x+2}{x-2}\).

Step 2 :We can use the long division method for polynomials. This method is similar to the long division method used for numbers. We divide the first term of the dividend by the first term of the divisor to find the first term of the quotient. Then we multiply the divisor by this term and subtract the result from the dividend to find the remainder. We repeat this process with the remainder as the new dividend until the degree of the remainder is less than the degree of the divisor.

Step 3 :By applying the long division method, we find that the quotient of the division is \(2x^2 + 7x - 3\).

Step 4 :Final Answer: The quotient of the long division is \(\boxed{2x^2 + 7x - 3}\).

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