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)%0D%0AResponses%0D%0A%0D%0A9h7−6h4+4%0D%0A9 h superscript 7 baseline minus 6 h superscript 4 baseline plus 4%0D%0A%0D%0A9h7−6h4%0D%0A9 h superscript 7 baseline minus 6 h superscript 4 baseline%0D%0A%0D%0A9h8−6h5+4h%0D%0A9 h superscript 8 baseline minus 6 h superscript 5 baseline plus 4 h%0D%0A%0D%0AThis rational expression does not have any equivalent forms.

Answer 1

To simplify the expression \( 27h^8 - 18h^5 + 12h^3h \), we first rewrite \( 12h^3h \) as \( 12h^4 \). So, the expression becomes:

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

Next, we can factor out the greatest common factor (GCF) from each term. The GCF of the coefficients \( 27, -18, \) and \( 12 \) is \( 9 \), and the lowest power of \( h \) is \( h^4 \). Therefore, we factor out \( 9h^4 \):

\[ 27h^8 - 18h^5 + 12h^4 = 9h^4(3h^4 - 2h + 1) \]

To check for equivalent forms among the provided options:

1. \( 9h^7 - 6h^4 + 4 \)
2. \( 9h^7 - 6h^4 \)
3. \( 9h^8 - 6h^5 + 4h \)
4. This rational expression does not have any equivalent forms.

The simplest equivalent form we have found through factoring is:

\[ 9h^4(3h^4 - 2h + 1) \]

However, none of the options provided match our factored form or the original expression. Therefore, we conclude that the correct response is:

This rational expression does not have any equivalent forms.