Let's match the given expressions with A, B, and C step-by-step.
1. We need to determine which given expression:
[tex]\[
A = -7 x^2 - 2 x + 5
\][/tex]
[tex]\[
B = 7 x^2 - 2 x + 7
\][/tex]
[tex]\[
C = 7 x^2 + 2 x - 5
\][/tex]
2. First expression:
[tex]\[
(3 x^2 - 6 x + 11) - (10 x^2 - 4 x + 6)
\][/tex]
Simplify this expression:
[tex]\[
3 x^2 - 6 x + 11 - 10 x^2 + 4 x - 6 = (3 x^2 - 10 x^2) + (-6 x + 4 x) + (11 - 6) = -7 x^2 - 2 x + 5
\][/tex]
The simplified expression matches with [tex]\( A \)[/tex].
3. Second expression:
[tex]\[
(-3 x^2 - 5 x - 3) - (-10 x^2 - 7 x + 2)
\][/tex]
Simplify this expression:
[tex]\[
-3 x^2 - 5 x - 3 + 10 x^2 + 7 x - 2 = (-3 x^2 + 10 x^2) + (-5 x + 7 x) + (-3 - 2) = 7 x^2 + 2 x - 5
\][/tex]
The simplified expression matches with [tex]\( C \)[/tex].
4. Third expression:
[tex]\[
(12 x^2 + 6 x - 5) - (5 x^2 + 8 x - 12)
\][/tex]
Simplify this expression:
[tex]\[
12 x^2 + 6 x - 5 - 5 x^2 - 8 x + 12 = (12 x^2 - 5 x^2) + (6 x - 8 x) + (-5 + 12) = 7 x^2 - 2 x + 7
\][/tex]
The simplified expression matches with [tex]\( B \)[/tex].
So, the complete statements are as follows:
[tex]\((3 x^2 - 6 x + 11) - (10 x^2 - 4 x + 6)\)[/tex] is equivalent to expression [tex]\( \mathbf{A} \)[/tex]
[tex]\(( -3 x^2 - 5 x - 3) - ( -10 x^2 - 7 x + 2)\)[/tex] is equivalent to expression [tex]\( \mathbf{C} \)[/tex]
[tex]\((12 x^2 + 6 x - 5) - (5 x^2 + 8 x - 12)\)[/tex] is equivalent to expression [tex]\( \mathbf{B} \)[/tex]
