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