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"