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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.
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.
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