Question

divide.
\\((16x^2 + 36x + 18) \div (2x + 3)\\)
your answer should give the quotient and the remainder.
quotient: \\(square\\)
remainder: \\(square\\)

Explanation:

Step1: Use polynomial long division

We divide \(16x^{2}+36x + 18\) by \(2x + 3\). First, divide the leading term of the dividend \(16x^{2}\) by the leading term of the divisor \(2x\), we get \(8x\).
Multiply the divisor \(2x + 3\) by \(8x\): \(8x(2x + 3)=16x^{2}+24x\)
Subtract this from the dividend: \((16x^{2}+36x + 18)-(16x^{2}+24x)=12x + 18\)

Step2: Divide the new leading term

Now, divide the leading term of \(12x\) (from the result of subtraction) by the leading term of the divisor \(2x\), we get \(6\).
Multiply the divisor \(2x + 3\) by \(6\): \(6(2x + 3)=12x+18\)
Subtract this from \(12x + 18\): \((12x + 18)-(12x + 18)=0\)

Answer:

Quotient: \(8x + 6\)
Remainder: \(0\)