Question

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

Answer 1

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"