Subtract these polynomials:

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

A. [tex]\(-2x^2 + 2x + 0\)[/tex]
B. [tex]\(6x^2 + 6x + 6\)[/tex]
C. [tex]\(6x^2 + 2x + 0\)[/tex]
D. [tex]\(-2x^2 + 6x + 6\)[/tex]



Answer :

To subtract the given polynomials, [tex]\((2x^2 + 4x + 3)\)[/tex] and [tex]\((4x^2 - 2x - 3)\)[/tex], we need to combine like terms by subtracting the corresponding coefficients of the second polynomial from the coefficients of the first polynomial. Here’s the step-by-step process:

1. Identify coefficients for each term:
- For [tex]\(2x^2 + 4x + 3\)[/tex]:
- Coefficient of [tex]\(x^2\)[/tex]: [tex]\(2\)[/tex]
- Coefficient of [tex]\(x\)[/tex]: [tex]\(4\)[/tex]
- Constant term: [tex]\(3\)[/tex]

- For [tex]\(4x^2 - 2x - 3\)[/tex]:
- Coefficient of [tex]\(x^2\)[/tex]: [tex]\(4\)[/tex]
- Coefficient of [tex]\(x\)[/tex]: [tex]\(-2\)[/tex]
- Constant term: [tex]\(-3\)[/tex]

2. Subtract the coefficients of corresponding terms:
- Coefficient of [tex]\(x^2\)[/tex]:
[tex]\[ 2 - 4 = -2 \][/tex]
- Coefficient of [tex]\(x\)[/tex]:
[tex]\[ 4 - (-2) = 4 + 2 = 6 \][/tex]
- Constant term:
[tex]\[ 3 - (-3) = 3 + 3 = 6 \][/tex]

3. Combine the results:
[tex]\[ (-2)x^2 + 6x + 6 \][/tex]

So, the result of subtracting the polynomials [tex]\((2x^2 + 4x + 3) - (4x^2 - 2x - 3)\)[/tex] is:
[tex]\[ -2x^2 + 6x + 6 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{D. \ -2x^2 + 6x + 6} \][/tex]