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Which of the following shows that polynomials are closed under subtraction when two polynomials, (5x2 + 2x − 6) − (3x2 − 6x + 2), are subtracted?

2x2 − 4x − 4; will be a polynomial
2x2 − 4x − 4; may or may not be a polynomial
2x2 + 8x − 8; will be a polynomial
2x2 + 8x − 8; may or may not be a polynomial

Respuesta :

Answer:

For [tex](2x^2 + 8x - 8)[/tex], the group is CLOSED as it a polynomial.

Step-by-step explanation:

Here, the given polynomials are:

[tex]P(x)=(5x^2+2x-6)\\Q(x)=(3x^2-6x+2)[/tex]

Now, a group G is said to be CLOSED UNDER SUBTRACTION if,

a and b are he elements of G ⇒ (a-b) is ALSO AN ELEMENT of G

Now, here:

[tex]R(x)  = P(x) - Q(x) = (5x^2+2x-6) - (3x^2-6x+2) = (2x^2 + 8x - 8)[/tex]

or, [tex]R(x)  = (2x^2 + 8x - 8)[/tex]

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  [tex](2x^2 + 8x - 8)[/tex], it will be a polynomial the group is CLOSED.

Answer:

The answer would be C

Step-by-step explanation:

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