Question

3
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{a}{b}\\) \\((\cdot)\\) \\(|a|\\) \\(a^b\\) (+) (-) (=) (\alpha) (\beta) (\zeta) (\delta) (\pi) \\(\sin) (\cos) (\tan) \\(\sin^{-1}\\)\\(\cos^{-1}\\)\\(\tan^{-1}) (\bar{0}) (\leftrightarrow) (\
ightarrow) (\angle) (\triangle) (n) (\sum)
\\(\sqrt{a}\\) \\(\sqrtn{a}\\) (a_0) (\cdot) (\times) (<) (>) (\leq) (\geq) (a) (\mu) (\
ho) (\varphi) (\csc) (\sec) (\cot) (\log) \\(\log_0) \\(\ln) (\parallel) (\perp) (\cong) (\sim) (^*) (u) \\(\

$$\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}$$

\\)
\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: \((12x^2 - 19x - 18) - (12x^2 + 8x) = -27x - 18\).

Step3: Divide the new leading term

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

Step4: Multiply and subtract again

Multiply the divisor \(3x + 2\) by \(-9\) to get \(-27x - 18\). Subtract this from \(-27x - 18\): \((-27x - 18) - (-27x - 18) = 0\).

Answer:

\(4x - 9\)