Sure! Let's find the sum of the expressions [tex]\(\left(3x^2 + 5x - 8\right)\)[/tex] and [tex]\(\left(5x^2 - 13x - 5\right)\)[/tex].
1. Identify the like terms in the given polynomials:
- The [tex]\(x^2\)[/tex] terms: [tex]\(3x^2\)[/tex] and [tex]\(5x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(5x\)[/tex] and [tex]\(-13x\)[/tex]
- The constant terms: [tex]\(-8\)[/tex] and [tex]\(-5\)[/tex]
2. Add the coefficients of the like terms:
- For the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2 + 5x^2\)[/tex]
[tex]\[
3x^2 + 5x^2 = 8x^2
\][/tex]
- For the [tex]\(x\)[/tex] terms: [tex]\(5x + (-13x)\)[/tex]
[tex]\[
5x - 13x = -8x
\][/tex]
- For the constant terms: [tex]\(-8 + (-5)\)[/tex]
[tex]\[
-8 - 5 = -13
\][/tex]
3. Combine the results to form the final polynomial:
[tex]\[
8x^2 - 8x - 13
\][/tex]
So, the sum of [tex]\(\left(3x^2 + 5x - 8\right)\)[/tex] and [tex]\(\left(5x^2 - 13x - 5\right)\)[/tex] is [tex]\(\boxed{8x^2 - 8x - 13}\)[/tex].
Therefore, the correct answer is:
C. [tex]\(\boxed{8x^2 - 8x - 13}\)[/tex]
