Answer :
To find the sum of the two given polynomials, let's break it down step by step:
We're adding these two polynomials:
1. [tex]\( (8x^2 + 5x + 3) \)[/tex]
2. [tex]\( (-5x^6 - 2x^5 - 4x^2 - 2x) \)[/tex]
Step 1: Identify and Combine Like Terms
1. [tex]\(x^6\)[/tex] terms:
- There is only one [tex]\(x^6\)[/tex] term: [tex]\(-5x^6\)[/tex].
2. [tex]\(x^5\)[/tex] terms:
- There is only one [tex]\(x^5\)[/tex] term: [tex]\(-2x^5\)[/tex].
3. [tex]\(x^2\)[/tex] terms:
- From the first polynomial, we have [tex]\(8x^2\)[/tex].
- From the second polynomial, we have [tex]\(-4x^2\)[/tex].
- Combine them: [tex]\(8x^2 + (-4x^2) = 4x^2\)[/tex].
4. [tex]\(x\)[/tex] terms:
- From the first polynomial, we have [tex]\(5x\)[/tex].
- From the second polynomial, we have [tex]\(-2x\)[/tex].
- Combine them: [tex]\(5x + (-2x) = 3x\)[/tex].
5. Constant terms:
- The constant term from the first polynomial is [tex]\(3\)[/tex].
- There is no constant term in the second polynomial, so the constant stays as [tex]\(3\)[/tex].
Step 2: Write the Resulting Polynomial
After combining the like terms, we get the polynomial:
[tex]\[ -5x^6 - 2x^5 + 4x^2 + 3x + 3 \][/tex]
This matches option C:
[tex]\[ -5x^6 - 2x^5 + 4x^2 + 3x + 3 \][/tex]
Therefore, the polynomial that represents the sum is:
C. [tex]\( -5x^6 - 2x^5 + 4x^2 + 3x + 3 \)[/tex]
We're adding these two polynomials:
1. [tex]\( (8x^2 + 5x + 3) \)[/tex]
2. [tex]\( (-5x^6 - 2x^5 - 4x^2 - 2x) \)[/tex]
Step 1: Identify and Combine Like Terms
1. [tex]\(x^6\)[/tex] terms:
- There is only one [tex]\(x^6\)[/tex] term: [tex]\(-5x^6\)[/tex].
2. [tex]\(x^5\)[/tex] terms:
- There is only one [tex]\(x^5\)[/tex] term: [tex]\(-2x^5\)[/tex].
3. [tex]\(x^2\)[/tex] terms:
- From the first polynomial, we have [tex]\(8x^2\)[/tex].
- From the second polynomial, we have [tex]\(-4x^2\)[/tex].
- Combine them: [tex]\(8x^2 + (-4x^2) = 4x^2\)[/tex].
4. [tex]\(x\)[/tex] terms:
- From the first polynomial, we have [tex]\(5x\)[/tex].
- From the second polynomial, we have [tex]\(-2x\)[/tex].
- Combine them: [tex]\(5x + (-2x) = 3x\)[/tex].
5. Constant terms:
- The constant term from the first polynomial is [tex]\(3\)[/tex].
- There is no constant term in the second polynomial, so the constant stays as [tex]\(3\)[/tex].
Step 2: Write the Resulting Polynomial
After combining the like terms, we get the polynomial:
[tex]\[ -5x^6 - 2x^5 + 4x^2 + 3x + 3 \][/tex]
This matches option C:
[tex]\[ -5x^6 - 2x^5 + 4x^2 + 3x + 3 \][/tex]
Therefore, the polynomial that represents the sum is:
C. [tex]\( -5x^6 - 2x^5 + 4x^2 + 3x + 3 \)[/tex]
