Divide. \[ \left(8 x^{2}+18 x+14\right) \div(2 x+3) \] Your answer should give the quotient and the remainder.

Step 1 ：Given the polynomial division problem \(\left(8 x^{2}+18 x+14\right) \div(2 x+3)\).

Step 2 ：We start by dividing the first term of the dividend \(8x^2\) by the first term of the divisor \(2x\) to find the first term of the quotient, which is \(4x\).

Step 3 ：Next, we multiply the divisor \(2x+3\) by this term \(4x\) and subtract the result from the dividend \(8x^2+18x+14\).

Step 4 ：The result of this subtraction is \(6x+14\).

Step 5 ：We then repeat the process, dividing the first term of the new dividend \(6x\) by the first term of the divisor \(2x\), which gives us the next term of the quotient, \(3\).

Step 6 ：Multiplying the divisor \(2x+3\) by this term \(3\) and subtracting the result from the new dividend \(6x+14\) gives us the remainder, \(5\).

Step 7 ：Since the degree of the remainder is less than the degree of the divisor, we stop here.

Step 8 ：The final quotient is \(4x+3\) and the remainder is \(5\).

Step 9 ：So, the solution to the polynomial division problem \(\left(8 x^{2}+18 x+14\right) \div(2 x+3)\) is the quotient \(\boxed{4x+3}\) and the remainder \(\boxed{5}\).