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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

Respuesta :

shoopdawhoopdedo
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"

ankitprmr2

When two polynomials [tex]4x^2 - 8x - 7[/tex] and [tex]-5x +16[/tex] are added, then the result is [tex]4x^2 - 13x + 9[/tex].  Thus, Option (A) is the correct option.

Let us determine the addition of the given polynomials.

[tex]\begin{aligned}\rm{Addition}&=4x^2 - 8x - 7+-5x+16\\&=4x^2 - 13x +9\end{aligned}[/tex]

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

Thus, the polynomial [tex]4x^2 - 13x + 9[/tex] is closed under addition when two polynomials [tex]4x^2 - 8x - 7[/tex] and [tex]-5x +16[/tex] are added.

Thus,

Option (A) is the correct option.

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

https://brainly.com/question/17822016

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