Answer:
For
, the group is CLOSED as it a polynomial.
Step-by-step explanation:
Here, the given polynomials are:
![P(x)=(5x^2+2x-6)\\Q(x)=(3x^2-6x+2)](https://tex.z-dn.net/?f=P%28x%29%3D%285x%5E2%2B2x-6%29%5C%5CQ%28x%29%3D%283x%5E2-6x%2B2%29)
Now, a group G is said to be <u>CLOSED UNDER SUBTRACTION</u> if,
a and b are he elements of G ⇒ (a-b) is ALSO AN ELEMENT of G
Now, here:
![R(x) = P(x) - Q(x) = (5x^2+2x-6) - (3x^2-6x+2) = (2x^2 + 8x - 8)](https://tex.z-dn.net/?f=R%28x%29%20%20%3D%20P%28x%29%20-%20Q%28x%29%20%3D%20%285x%5E2%2B2x-6%29%20-%20%283x%5E2-6x%2B2%29%20%3D%20%282x%5E2%20%2B%208x%20-%208%29)
or, ![R(x) = (2x^2 + 8x - 8)](https://tex.z-dn.net/?f=R%28x%29%20%20%3D%20%282x%5E2%20%2B%208x%20-%208%29)
Also, R(x) is a POLYNOMIAL.
So, R(x) is an Element of group G.
So, the set G of polynomials.
Hence, for the polynomial
, it will be a polynomial the group is CLOSED.