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Use the long division method to find the result when $4 x^{3}+7 x^{2}-17 x-7$ is divided by $4 x+3$. If there is a remainder, express the result in the form $q(x)+\frac{r(x)}{b(x)}$.
Answer

Step 1 ：\(4x^3 + 7x^2 - 17x - 7 \div 4x + 3\)

Step 2 ：\(4x^3 ÷ 4x = x^2\)

Step 3 ：\((4x + 3)x^2 = 4x^3 + 3x^2\)

Step 4 ：\(4x^3 + 7x^2 - (4x^3 + 3x^2) = 4x^2 - 17x - 7\)

Step 5 ：\(4x^2 ÷ 4x = x\)

Step 6 ：\((4x + 3)x = 4x^2 + 3x\)

Step 7 ：\(4x^2 - 17x - (4x^2 + 3x) = -20x - 7\)

Step 8 ：\(-20x ÷ 4x = -5\)

Step 9 ：\((4x + 3)(-5) = -20x - 15\)

Step 10 ：\(-20x - 7 - (-20x - 15) = 8\)

Step 11 ：\(\boxed{x^2 + x - 5 + \frac{8}{4x + 3}}\)