Myrna was asked to create an equivalent form of the rational expression 56k^7-14k^3+14/7k^3. Which of the following is a correct equivalent form?
The rational expression 56k^7 - 14k^3 + 14/7k^3 can be simplified by factoring out the greatest common factor (GCF) of the terms in the numerator, which is 14:
= 14(4k^7 - k^3 + 1/7k^3)
Option: 14(4k^7 - k^3 + 1/7k^3)
To create an equivalent form for the rational expression, we can factor out the common factor in the numerator and denominator.
The common factor in the numerator and the denominator is 7k^3, so we can factor it out:
56k^7 - 14k^3 + 14 / 7k^3
= (7k^3)(8k^4 - 2 + 2 / 1)
Simplifying the expression further,
= 7k^3(8k^4 - 2 + 2/1)
So, the correct equivalent form of the rational expression is 7k^3(8k^4 - 2 + 2/1).
To find an equivalent form of the given rational expression, we need to simplify it.
The expression is: 56k^7 - 14k^3 + 14 / 7k^3
First, let's factor out the greatest common factor (GCF) of the numerator. The GCF is 14:
14(4k^7 - k^3 + 1) / 7k^3
Now, let's simplify the expression further. Notice that we can divide both the numerator and denominator by 14:
(4k^7 - k^3 + 1) / (7k^3)
Therefore, the correct equivalent form of the given rational expression is (4k^7 - k^3 + 1) / (7k^3).