Perform the indicated operation. Give your answer in descending powers of [tex] x [/tex].

[tex]
\left(6x^2 - 4x + 11\right) + \left(4 - x^2 - 3x\right)
[/tex]

A. [tex] 7x^2 - x + 7 [/tex]

B. [tex] 5x^2 - 7x + 15 [/tex]

C. [tex] 5x^2 - 7x + 15 [/tex]

D. [tex] 15 - 7x + 5x^2 [/tex]

E. [tex] 7 - x + 7x^2 [/tex]

Sure! Let's perform the operation step-by-step to find the sum of the polynomials [tex]\((6x^2 - 4x + 11)\)[/tex] and [tex]\((4 - x^2 - 3x)\)[/tex], and express the result in descending powers of [tex]\(x\)[/tex].

1. Write down the polynomials:
- First polynomial: [tex]\(6x^2 - 4x + 11\)[/tex]
- Second polynomial: [tex]\(4 - x^2 - 3x\)[/tex]

2. Arrange the second polynomial in standard form:
- [tex]\(4 - x^2 - 3x\)[/tex] can be rewritten as [tex]\(-x^2 - 3x + 4\)[/tex] for easier addition.

3. Add the corresponding terms from both polynomials:

- [tex]\(x^2\)[/tex] terms:
- [tex]\(6x^2\)[/tex] from the first polynomial, [tex]\(-x^2\)[/tex] from the second polynomial.
- [tex]\(6x^2 + (-x^2) = 5x^2\)[/tex]

- [tex]\(x\)[/tex] terms:
- [tex]\(-4x\)[/tex] from the first polynomial, [tex]\(-3x\)[/tex] from the second polynomial.
- [tex]\(-4x + (-3x) = -7x\)[/tex]

- Constant terms:
- [tex]\(11\)[/tex] from the first polynomial, [tex]\(4\)[/tex] from the second polynomial.
- [tex]\(11 + 4 = 15\)[/tex]

4. Combine the results:
- The resulting polynomial is [tex]\(5x^2 - 7x + 15\)[/tex].

So, the final answer in descending powers of [tex]\(x\)[/tex] is:
[tex]\[ 5x^2 - 7x + 15 \][/tex]