College

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.