Problem
![\text{State the symmetry of f(x) = x}^4+2x^3\text{ - 4x}](https://tex.z-dn.net/?f=%5Ctext%7BState%20the%20symmetry%20of%20f%28x%29%20%3D%20x%7D%5E4%2B2x%5E3%5Ctext%7B%20-%204x%7D)
Method
A symmetric function is a function in several variable which remain unchanged for any permutation of the variables.
f(-x) = f(x)
Final answer
![\begin{gathered} f(x)=x^4+2x^3\text{ - 4x} \\ \\ f(-x)\text{ = }x^4+2(-x)^3\text{ - 4(-x)} \\ f(-x)=x^4-2x^3\text{ + 4x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%28x%29%3Dx%5E4%2B2x%5E3%5Ctext%7B%20-%204x%7D%20%5C%5C%20%20%5C%5C%20f%28-x%29%5Ctext%7B%20%3D%20%7Dx%5E4%2B2%28-x%29%5E3%5Ctext%7B%20-%204%28-x%29%7D%20%5C%5C%20f%28-x%29%3Dx%5E4-2x%5E3%5Ctext%7B%20%2B%204x%7D%20%5Cend%7Bgathered%7D)
from the final solution
Answer:
The answer is "
".
Step-by-step explanation:
In this question, it can measure this using the following step if you'd like to find the missing element in both types of parentheses:
![\to 10x^3 + 35x^2 - 4x - 14 \\\\\to (5x^2-2) (2x+7)\\\\\to 5x^2 (2x + 7) - 2 (2x + 7)\\](https://tex.z-dn.net/?f=%5Cto%2010x%5E3%20%2B%2035x%5E2%20-%204x%20-%2014%20%5C%5C%5C%5C%5Cto%20%285x%5E2-2%29%20%282x%2B7%29%5C%5C%5C%5C%5Cto%20%205x%5E2%20%282x%20%2B%207%29%20-%202%20%282x%20%2B%207%29%5C%5C)
So, the correct answer would be (2x + 7).