To find \( f(x) - g(x) \) where \( f(x) = 3x^2 - 4x + 5 \) and \( g(x) = 2x^2 + 2 \), follow these steps:
1. Arrange the expressions for \( f(x) \) and \( g(x) \):
[tex]\[
f(x) = 3x^2 - 4x + 5
\][/tex]
[tex]\[
g(x) = 2x^2 + 2
\][/tex]
2. Subtract the like terms of \( f(x) \) and \( g(x) \):
- \( x^2 \) terms: \( 3x^2 - 2x^2 = 1x^2 \)
- \( x \) terms: \( -4x \)
- Constant terms: \( 5 - 2 = 3 \)
3. Combine the results from step 2 to form the polynomial \( f(x) - g(x) \):
[tex]\[
f(x) - g(x) = 1x^2 - 4x + 3
\][/tex]
So, \( f(x) - g(x) \) is:
[tex]\[
\boxed{x^2 - 4x + 3}
\][/tex]
Checking the choices:
A. \( 5x^2 - 4x + 7 \)
B. \( x^2 - 4x + 3 \)
C. \( -x^2 + 4x - 3 \)
D. \( x^2 - 4x + 7 \)
Thus, the correct answer is option [tex]\( \boxed{B} \)[/tex].
