To subtract the polynomials [tex]\((7x^2 - 5x + 3) - (2x^2 + 7x - 4)\)[/tex], we need to subtract the coefficients of like terms step by step.
### Step-by-Step Solution
1. Align the polynomials to make sure we subtract each corresponding coefficient:
[tex]\[
\begin{array}{r}
7x^2 - 5x + 3 \\
-\quad(2x^2 + 7x - 4) \\
\hline
\end{array}
\][/tex]
2. Distribute the negative sign across the second polynomial when subtracting each term:
[tex]\[
7x^2 - 5x + 3 - (2x^2 + 7x - 4) = 7x^2 - 5x + 3 - 2x^2 - 7x + 4
\][/tex]
3. Combine like terms:
- [tex]\(x^2\)[/tex] terms: [tex]\(7x^2 - 2x^2 = 5x^2\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(-5x - 7x = -12x\)[/tex]
- Constant terms: [tex]\(3 + 4 = 7\)[/tex]
Putting it all together, we get:
[tex]\[
5x^2 - 12x + 7
\][/tex]
### Conclusion
The resulting polynomial after subtraction is [tex]\(5x^2 - 12x + 7\)[/tex].
Therefore, the correct choice is:
B. [tex]\(5x^2 - 12x + 7\)[/tex]
