To find the sum of the polynomials [tex]\((3x^3 - 5x - 8) + (5x^3 + 7x + 3)\)[/tex], we will add the corresponding coefficients of each term.
1. Identify and arrange the terms of the polynomials:
- [tex]\(3x^3 - 5x - 8\)[/tex]
- [tex]\(5x^3 + 7x + 3\)[/tex]
2. Add the coefficients of the [tex]\(x^3\)[/tex] terms:
[tex]\[
3 + 5 = 8
\][/tex]
Therefore, the [tex]\(x^3\)[/tex] term in the sum is [tex]\(8x^3\)[/tex].
3. Add the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[
-5 + 7 = 2
\][/tex]
Therefore, the [tex]\(x\)[/tex] term in the sum is [tex]\(2x\)[/tex].
4. Add the constant terms:
[tex]\[
-8 + 3 = -5
\][/tex]
Therefore, the constant term in the sum is [tex]\(-5\)[/tex].
Combining these results, we get the polynomial:
[tex]\[
8x^3 + 2x - 5
\][/tex]
Thus, the correct sum of the polynomials [tex]\((3x^3 - 5x - 8) + (5x^3 + 7x + 3)\)[/tex] is [tex]\[
8x^3 + 2x - 5.
\][/tex]
Hence, the correct answer is:
[tex]\[
8x^3 + 2x - 5.
\][/tex]
