Question

divide.
\\((54x^2 + 45x + 8) \div (3x + 2)\\)
your answer should give the quotient and the remainder.
quotient: \\(\square\\)
remainder: \\(\square\\)

Explanation:

Step1: Divide the leading terms

Divide the leading term of the dividend \(54x^2\) by the leading term of the divisor \(3x\). So, \(\frac{54x^2}{3x} = 18x\). This is the first term of the quotient.

Step2: Multiply and subtract

Multiply the divisor \(3x + 2\) by \(18x\): \(18x(3x + 2)=54x^2 + 36x\). Subtract this from the dividend: \((54x^2 + 45x + 8)-(54x^2 + 36x)=9x + 8\).

Step3: Divide the new leading term

Divide the leading term of the new dividend \(9x\) by the leading term of the divisor \(3x\). So, \(\frac{9x}{3x}=3\). This is the second term of the quotient.

Step4: Multiply and subtract again

Multiply the divisor \(3x + 2\) by \(3\): \(3(3x + 2)=9x + 6\). Subtract this from the new dividend \(9x + 8\): \((9x + 8)-(9x + 6)=2\). This is the remainder.

Answer:

Quotient: \(18x + 3\)
Remainder: \(2\)