use the provided answers

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 find an equivalent form of the rational expression $27h^8-18h^5+12h^3$, we can factor out the greatest common factor (GCF) from the terms.

1. The coefficients are 27, -18, and 12. The GCF of these coefficients is 9.
2. The terms all contain varying powers of $h$. The lowest power of $h$ in the expression is $h^3$.

Thus, we can factor out $9h^3$:

$$27h^8-18h^5+12h^3=9h^3(3h^5-2h^2+1)$$

Now we can rewrite it in different forms. However, if we simplify further by factoring or combining terms while maintaining equivalent expressions, we need to verify the provided options:

1. Option A: $9h^7-6h^4$ does not represent the original expression.
2. Option B: This says the rational expression has no equivalent forms, which is incorrect because we just factored it.
3. Option C: $9h^8-6h^5+4h$ does not match the expression.
4. Option D: $9h^7-6h^4+4$ does not represent the original expression.

None of the provided options are correct. The simplest equivalent form based on our factoring could be stated as:

$$9h^3(3h^5-2h^2+1)$$

If you need to select one despite them being incorrect, you should note that no accurate equivalent representation was provided in your choices.