myrna was asked to create an equivalent form of the rational expression 56k^7-14k^3+14/7k^3. which of the following is the correct equivalent
(1 point)
Responses
8k4−2k+2k3
8 k to the 4th power minus 2 k plus the fraction with numerator 2 and denominator k cubed
8k4−2+2k3
8 k to the 4th power minus 2 plus the fraction with numerator 2 and denominator k cubed
8k4+2k3
8 k to the 4th power plus the fraction with numerator 2 and denominator k cubed
8k10−2k6+2k3
The correct equivalent form of the rational expression is 8k^4 - 2 + 2k^3.
To create an equivalent form of the given rational expression, we need to simplify the numerator. The numerator is 56k^7 - 14k^3 + 14.
To simplify this, we look for the common factors in the terms of the numerator. In this case, 14 is a common factor, so we can factor it out:
Numerator: 14(4k^7 - k^3 + 1)
Now, let's look at the answer choices:
1) 8k^4 - 2k + 2k^3
2) 8k^4 - 2 + 2k^3
3) 8k^4 + 2k^3
4) 8k^10 - 2k^6 + 2k^3
Comparing the answer choices to our simplified numerator, we can eliminate options 1, 2, and 4 because they don't match the form 14(4k^7 - k^3 + 1).
The correct answer is option 3) 8k^4 + 2k^3. This matches the form of the simplified numerator.
Therefore, the correct equivalent form of the given rational expression is 8k^4 + 2k^3.
To create an equivalent form of the rational expression 56k^7-14k^3+14/7k^3, you need to simplify it.
First, factor out the greatest common factor from the expression:
GCF: 7k^3
56k^7-14k^3+14/7k^3 = (7k^3)(8k^4-2+2/7)
Therefore, the correct equivalent form is:
8k^4-2+2/7k^3