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)

Question

Responses

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

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

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

9h7−6h4

Answer 1

To create an equivalent form of the rational expression \( 27h^8 - 18h^5 + 12h^3 \), we can factor it.

Let's factor out the greatest common factor (GCF) from the terms:

1. The GCF of the coefficients (27, -18, 12) is 9.
2. The smallest power of \( h \) in \( h^8, h^5, h^3 \) is \( h^3 \).

Thus, we can factor out \( 9h^3 \):

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

Now, let's check if the given responses correspond to an equivalent form.

1. \( 9h^7 - 6h^4 + 4 \) does not correspond to our factored form.
2. \( 9h^8 - 6h^5 + 4h \) does not correspond to our factored form.
3. "This rational expression does not have any equivalent forms." This is incorrect since we can factor the expression.
4. \( 9h^7 - 6h^4 \) does not correspond to our factored form.

From the given options, none of them represent a correct equivalent form of the rational expression after factoring.

Thus, I conclude that while it is incorrect to claim that the expression does not have any equivalent forms, none of the provided options accurately represent an equivalent form of the original expression.