Subtract these polynomials:

[tex]\[
(3x^2 + 6x + 7) - (6x^2 - 5x - 7) =
\][/tex]

A. [tex]\(-3x^2 + x + 0\)[/tex]

B. [tex]\(-3x^2 + 11x + 14\)[/tex]

C. [tex]\(9x^2 + x + 0\)[/tex]

D. [tex]\(9x^2 + 11x + 14\)[/tex]



Answer :

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]