College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Find the sum of the polynomials below:

[tex]\[
\left(8x^9 + 4x - 4\right) + \left(5x^9 + x + 5\right)
\][/tex]

A. [tex]\(13x^9 + 5x + 1\)[/tex]

B. [tex]\(13x^9 - 5x + 1\)[/tex]

C. [tex]\(40x^{18} + 5x^2 + 1\)[/tex]

D. [tex]\(40x^9 + 4x^2 + 1\)[/tex]

Answer :

To find the sum of the two polynomials, we will add them term by term. Let's break it down:

The polynomials given are:
1. [tex]\(8x^9 + 4x - 4\)[/tex]
2. [tex]\(5x^9 + x + 5\)[/tex]

Step 1: Combine the [tex]\(x^9\)[/tex] terms

For the [tex]\(x^9\)[/tex] terms, we add the coefficients:
- The coefficient of [tex]\(x^9\)[/tex] in the first polynomial is 8.
- The coefficient of [tex]\(x^9\)[/tex] in the second polynomial is 5.

So, [tex]\(8 + 5 = 13\)[/tex]. This gives us a [tex]\(13x^9\)[/tex] term.

Step 2: Combine the [tex]\(x\)[/tex] terms

For the [tex]\(x\)[/tex] terms, we add the coefficients:
- The coefficient of [tex]\(x\)[/tex] in the first polynomial is 4.
- The coefficient of [tex]\(x\)[/tex] in the second polynomial is 1.

So, [tex]\(4 + 1 = 5\)[/tex]. This gives us a [tex]\(5x\)[/tex] term.

Step 3: Combine the constant terms

For the constant terms, we add them directly:
- The constant term in the first polynomial is -4.
- The constant term in the second polynomial is 5.

So, [tex]\(-4 + 5 = 1\)[/tex].

Putting it all together:

We've combined each corresponding term, which results in the polynomial:
[tex]\[13x^9 + 5x + 1\][/tex]

Therefore, the sum of the polynomials is:
[tex]\[ \boxed{13x^9 + 5x + 1} \][/tex]

This corresponds to option A.