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?
8k^4 - 2k + 2/k^3
8k^4 + 2/k^3
8k^10 - 2k^6 + 2/k^3
8k^4 - 2 + 2/k^3
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.
To create an equivalent form of the given rational expression, we need to simplify the expression.
Given expression: (56k^7 - 14k^3 + 14) / (7k^3)
We can simplify the expression as follows:
= 14 (4k^7 - k^3 + 1) / (7k^3)
= 2 (4k^7 - k^3 + 1) / k^3
So, the correct equivalent form is: 2 (4k^7 - k^3 + 1) / k^3
Therefore, none of the options provided match the correct equivalent form of the given expression.
To find the equivalent form of the given rational expression, we need to simplify it by factoring and reducing if possible.
The given rational expression is: (56k^7 - 14k^3 + 14) / (7k^3)
To find a common factor, we can factor out 14 from the numerator:
56k^7 - 14k^3 + 14 = 14(4k^7 - k^3 + 1)
Now, let's try to factor the remaining expression inside the parentheses. The expression resembles a quadratic in terms of k^4:
4k^7 - k^3 + 1
To factor this expression, we can substitute a variable to make it easier to work with. Let's set u = k^4:
4u^2 - u + 1
Unfortunately, this expression cannot be factored further using integer coefficients, so the expression (4k^7 - k^3 + 1) remains as it is.
Now, let's put everything back together:
The original rational expression: (56k^7 - 14k^3 + 14) / (7k^3)
After factoring the numerator: (14(4k^7 - k^3 + 1)) / (7k^3)
Therefore, the correct equivalent form of the given expression is: 2(4k^7 - k^3 + 1) / (7k^3).
From the given answer choices, the correct equivalent form is: 8k^4 - 2k + 2/k^3.