Question

Which of the following is a simplified, equivalent form of the rational expression 5x3−8x2+34x2 ?(1 point)
Responses
5x5/4−2x4+3/4x2
5x3/4−2x2+3/4x2
5x/4+3/4x2
5x/4−2+3/4x2

Answer 1

To simplify the expression \(5x^3 - 8x^2 + 34x^2\), we first need to combine like terms.

The term \( -8x^2\) and \( +34x^2\) can be combined:

\[
-8x^2 + 34x^2 = 26x^2
\]

So the expression simplifies to:

\[
5x^3 + 26x^2
\]

Next, this can be factored to identify common factors if possible:

\[
x^2(5x + 26)
\]

Now, let’s compare this with the provided answer options:

- \( \frac{5x^5}{4} - 2x^4 + \frac{3}{4}x^2 \)
- \( \frac{5x^3}{4} - 2x^2 + \frac{3}{4}x^2 \)
- \( \frac{5x}{4} + \frac{3}{4}x^2 \)
- \( \frac{5x}{4} - 2 + \frac{3}{4}x^2 \)

None of the options provided directly match or are equivalent to the simplified form \(x^2(5x + 26)\) or \(5x^3 + 26x^2\).

It seems there might be a misunderstanding or a typo in the expression that was provided because none of the options accurately represent the simplification of \(5x^3 - 8x^2 + 34x^2\).

If there is a need to further interpret or clarify your question based on the answers, please let me know!