Question

Myrna was asked to create an equivalent form of the rational expression 56k7−14k3+147k3
. Which of the following is a correct equivalent form?(1 point)
Responses

8k4−2k+2k3
8 superscript k 4 baseline minus 2 k plus Start Fraction 2 over k cubed End Fraction

8k10−2k6+2k3
8 superscript k 10 baseline minus 2 superscript 6 baseline plus Start Fraction 2 over k cubed End Fraction

8k4−2+2k3
8 superscript k 4 baseline minus 2 plus Start Fraction 2 over k cubed End Fraction

8k4+2k3

Answer 1

To simplify the expression \( 56k^7 - 14k^3 + 147k^3 \), we need to combine like terms and factor if possible.

First, let's combine the second and third terms:

\[
-14k^3 + 147k^3 = (147 - 14)k^3 = 133k^3
\]

So now, the expression becomes:

\[
56k^7 + 133k^3
\]

Next, let's factor out the greatest common factor (GCF) from the entire expression. The GCF of \( 56k^7 \) and \( 133k^3 \) is \( 7k^3 \).

We can factor \( 7k^3 \) out of the expression:

\[
56k^7 + 133k^3 = 7k^3(8k^4 + 19)
\]

Thus, the simplified equivalent form is:

\[
7k^3(8k^4 + 19)
\]

Now let's compare it to the options given:

1. \( 8k^4 - 2k + 2k^3 \)
2. \( 8k^{10} - 2k^6 + 2k^3 \)
3. \( 8k^4 - 2 + 2k^3 \)
4. \( 8k^4 + 2k^3 \)

None of these options directly show the correct equivalent form \( 7k^3(8k^4 + 19) \), but if we only consider terms without factoring, \( 8k^4 + 2k^3 \) contains the terms \( 8k^4 \) and \( 2k^3 \), which resembles part of our expression. However, it does not account for the factor of \( 7k^3 \) accurately.

Given the available options and the work done, none of the provided responses accurately represent the correctly simplified form. If you're required to select one based on its closest resemblance to common factors/terms, choose:

**8k^4 + 2k^3** as the most similar option based on the top-level polynomial comparison, though it does not preserve the necessary coefficients or full factorization.