If you're not sure how to simplify the given expression, you can solve this question by testing values.

Since we're looking for an equivalent expression, both the given expression and the correct answer must evaluate to have the same value for any value of x.

So, for example, if \(x = 2\), then \(\frac{6x^3 + 3x^2 - 8x - 4}{2x + 1} =\frac{6(2)^3 + 3(2)^2 - 8(2) - 4}{2(2) + 1}\)

\(=\frac{48 + 12 - 16 - 4}{4 + 1}\)

\(=\frac{40}{5}\)

\(=8\)

This tells us that, the correct answer must also evaluate to be \(8\) when \(x = 2\)

So let's plug \(x = 2\) into each answer choice and see which expression evaluates to be \(8\)

A. \(3(2)^2 + \frac{3}{2}(2) -8=7\). No good. We need the expression to evaluate to be \(8\)

B. \(3(2)^2 + \frac{3}{2}(2) -4=11\). No good. We need the expression to evaluate to be \(8\)

C. \(3(2^2) – 4=8\). Woo woo!!!

D. \(3(2) – 4=2\). No good. We need the expression to evaluate to be \(8\)

E. \(3(2) + 4=10\). No good. We need the expression to evaluate to be \(8\)

Answer: C

Cheers,
Brent