Question

find the quotient.
\\(\frac{-6a^4 + 18a^3 + 12a}{-3a}\\)
enter the correct answer.

Explanation:

Step1: Divide each term by \(-3a\)

We have the numerator \(-6a^4 + 18a^3 + 12a\) and the denominator \(-3a\). We will divide each term in the numerator by the denominator.

For the first term: \(\frac{-6a^4}{-3a}\)
When dividing variables with exponents, we subtract the exponents: \(a^{4 - 1}=a^3\). And for the coefficients: \(\frac{-6}{-3} = 2\). So the first term is \(2a^3\).

For the second term: \(\frac{18a^3}{-3a}\)
The coefficient: \(\frac{18}{-3}=-6\). The variable part: \(a^{3 - 1}=a^2\). So the second term is \(-6a^2\).

For the third term: \(\frac{12a}{-3a}\)
The coefficient: \(\frac{12}{-3}=-4\). The variable part: \(a^{1 - 1}=a^0 = 1\) (since any non - zero number to the power of 0 is 1). So the third term is \(-4\).

Step2: Combine the terms

Now we combine the results of the three divisions: \(2a^3-6a^2 - 4\)

Answer:

\(2a^{3}-6a^{2}-4\)