Question
use the provided answers
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
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
Answers
GPT-4o mini
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.
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.