Question

Marissa was asked to create an equivalent form of the rational expression 27h8−18h5+12h3h . Which of the following is a correct equivalent form?(1 point)
Responses

9h7−6h4
9 h superscript 7 baseline minus 6 h superscript 4 baseline

This rational expression does not have any equivalent forms.
This rational expression does not have any equivalent forms.

9h8−6h5+4h
9 h superscript 8 baseline minus 6 h superscript 5 baseline plus 4 h

9h7−6h4+4
9 h superscript 7 baseline minus 6 h superscript 4 baseline plus 4

Answer 1

To determine an equivalent form of the given rational expression \( 27h^8 - 18h^5 + 12h^3h \), we first simplify it.

The term \( 12h^3h \) can be simplified to \( 12h^4 \). So, we rewrite the expression:

\[
27h^8 - 18h^5 + 12h^4
\]

Next, we look for a common factor in the expression \( 27h^8 - 18h^5 + 12h^4 \). The greatest common factor (GCF) of the coefficients \( 27, -18, \) and \( 12 \) is \( 9 \), and the common factor in terms of \( h \) is \( h^4 \).

Factoring \( 9h^4 \) out of each term gives:

\[
9h^4(3h^4 - 2h + 1.33)
\]

However, for convenience, let’s factor it in a simpler way:

1. \( 27h^8 \) becomes \( 9h^4 \cdot 3h^4 \)
2. \( -18h^5 \) becomes \( 9h^4 \cdot (-2h) \)
3. \( 12h^4 \) becomes \( 9h^4 \cdot \frac{4}{3} \)

Our factored form is:

\[
9h^4(3h^4 - 2h + \frac{4}{3})
\]

As we break it down, we can analyze the options given:

1. \( 9h^7 - 6h^4 \)
2. \( 9h^8 - 6h^5 + 4h \)
3. \( 9h^7 - 6h^4 + 4 \)

None of these options match our final factored outcome directly.

To evaluate them further:
- \( 9h^7 - 6h^4 \) does not have a term to represent \( 27h^8 \) or \( -18h^5 + 12h^4 \).
- \( 9h^8 - 6h^5 + 4h \) includes a wrong coefficient for \( h^8 \) and an incorrect arrangement for \( h^5\) and \( h^4 \).
- \( 9h^7 - 6h^4 + 4 \) is also incorrect based on dimensionality and coefficient validations.

Therefore, the conclusion is:

This rational expression does not have any equivalent forms as per the options provided.