Question

5
enter the correct answer in the box.
use long division to determine the quotient of the following expression.
$(12x^2 - 19x - 18) \div (3x + 2)$
write the quotient in standard form with the term of largest degree on the left.
\\(\frac{□}{□}\\) (0) |0| \\(□^□\\) + − = π α β γ δ sin cos tan \\(\sin^{-1}\\) \\(\cos^{-1}\\) \\(\tan^{-1}\\) \\(\bar{0}\\) ←→ → ∠ △ n ℤ
\\(\sqrt{□}\\) \\(\sqrt□{□}\\) \\(□_□\\) ⋅ × < > ≤ ≥ λ μ ρ φ csc sec cot log \\(\log_{□}\\) ln ∥ 1 ≈ ~ ⋅ ∪ \\(\int_{□}^{□}\\)
\\(\boxed{}\\)

Explanation:

Step1: Divide the leading terms

Divide the leading term of the dividend \(12x^2\) by the leading term of the divisor \(3x\). So, \(\frac{12x^2}{3x} = 4x\).

Step2: Multiply and subtract

Multiply the divisor \(3x + 2\) by \(4x\) to get \(12x^2 + 8x\). Subtract this from the dividend: \((12x^2 - 19x - 18) - (12x^2 + 8x) = 12x^2 - 19x - 18 - 12x^2 - 8x = -27x - 18\).

Step3: Divide the new leading terms

Divide the leading term of \(-27x\) by \(3x\), which gives \(\frac{-27x}{3x} = -9\).

Step4: Multiply and subtract again

Multiply the divisor \(3x + 2\) by \(-9\) to get \(-27x - 18\). Subtract this from \(-27x - 18\): \((-27x - 18) - (-27x - 18) = -27x - 18 + 27x + 18 = 0\). There is no remainder.

Answer:

\(4x - 9\)