Myrna was asked to create an equivalent form of the rational expression 56k^7-14k^3+14/7k^3. Which of the following answers is a correct equivalent form?

Question

8k^4 - 2k + 2/k^3

8k^4 + 2/k^3

8k^10 - 2k^6 + 2/k^3

8k^4 - 2 + 2/k^3

Answer 1

To create an equivalent form of the rational expression, we can simplify it by factoring out the common factor from the numerator.

The numerator of the expression is 56k^7 - 14k^3 + 14. The common factor in this expression is 14. Factoring out 14 from the numerator, we get:

14(4k^7 - k^3 + 1).

Now, we can rewrite the expression as:

14(4k^7 - k^3 + 1) / 7k^3.

Simplifying further, we can cancel out the common factor of 7 between the numerator and the denominator, resulting in:

2(4k^7 - k^3 + 1) / k^3.

Therefore, the correct equivalent form of the given rational expression is:

2(4k^7 - k^3 + 1) / k^3.

None of the answer choices provided match this equivalent form, so the given options are incorrect.