Which of the following shows that polynomials are closed under addition when two polynomials 4x2 − 8x − 7 and −5x + 16 are added?
a. 4x^2 - 13x + 9 may or may not be a polynomial
b. 4x^2 + 13x -23 may or may not be a polynomial
c. 4x^2 -13x + 9 will be a polynomial
d. 4x^2 + 13x - 23 will be a polynomial

First we have to combine like terms. 4x² is one term. -8x is another term. -7 is another term. poly = "many" ⇒ polynomial = many terms

(4x² - 8x - 7) + (-5x + 16)

4x² - 8x - 7 - 5x + 16

Combine like terms.
Step 1: 4x² has no other terms with x² so it stays by itself.
Step 2: -8x and -5x are like terms because they both have x.
So -8x -5x = -13x (You put two negatives together)
Step 3: -7 and 16 don't have any x with them. -7 + 16 = 16 - 7 = 9

Now we put all the answers of the steps together.
Step 1: 4x²
Step 2: -13x
Step 3: 9

So the answer is 4x² - 13x +9
And it's a polynomial because there are three terms = "more than one term"

When two polynomials and are added, then the result is .  Thus, Option (A) is the correct option.

Let us determine the addition of the given polynomials.

Now, check all the options and see which option is perfectly matched with our final expression.

Thus, the polynomial is closed under addition when two polynomials and are added.

Thus,

Option (A) is the correct option.

To know more about the polynomials, please refer to the link:

link

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Step-by-step explanation: