Certainly! Let's work through the problem step-by-step.
We have two polynomials that we need to subtract:
[tex]\[
\left(3x^2 + 6x + 7\right) - \left(6x^2 - 5x - 7\right)
\][/tex]
To subtract these polynomials, we need to distribute the negative sign to each term in the second polynomial, and then combine like terms with the first polynomial. Let's break it down:
1. Distribute the negative sign to each term in the second polynomial:
[tex]\[
3x^2 + 6x + 7 - 6x^2 + 5x + 7
\][/tex]
2. Now, combine the like terms by subtracting the coefficients of corresponding powers of [tex]\(x\)[/tex]:
- For [tex]\(x^2\)[/tex] terms:
[tex]\[ 3x^2 - 6x^2 = (3 - 6)x^2 = -3x^2 \][/tex]
- For [tex]\(x\)[/tex] terms:
[tex]\[ 6x + 5x = (6 + 5)x = 11x \][/tex]
- For the constant terms:
[tex]\[ 7 + 7 = 14 \][/tex]
Putting it all together, we get:
[tex]\[
-3x^2 + 11x + 14
\][/tex]
Thus, the result of subtracting the given polynomials is [tex]\(-3x^2 + 11x + 14\)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{-3x^2 + 11x + 14}
\][/tex]
This corresponds to option B.
So, the answer is:
B. [tex]\(-3x^2 + 11x + 14\)[/tex]
