To simplify the given expression [tex]\(\left(11 m^2-7\right) - \left(6 m^2 + 3 m - 11\right) + \left(3 m^2 - m - 9\right)\)[/tex], we can follow these steps:
1. Distribute the negative sign to simplify the expression:
[tex]\[
(11m^2 - 7) - (6m^2 + 3m - 11) + (3m^2 - m - 9)
\][/tex]
This will give us:
[tex]\[
11m^2 - 7 - 6m^2 - 3m + 11 + 3m^2 - m - 9
\][/tex]
2. Combine like terms:
- For the [tex]\(m^2\)[/tex] terms:
[tex]\[
11m^2 - 6m^2 + 3m^2
\][/tex]
Combining these, we get:
[tex]\[
(11 - 6 + 3)m^2 = 8m^2
\][/tex]
- For the [tex]\(m\)[/tex] terms:
[tex]\[
-3m - m
\][/tex]
Combining these, we get:
[tex]\[
(-3 - 1)m = -4m
\][/tex]
- For the constant terms:
[tex]\[
-7 + 11 - 9
\][/tex]
Combining these, we get:
[tex]\[
-7 + 11 - 9 = -5
\][/tex]
Therefore, the simplified form of the expression is:
[tex]\[
8m^2 - 4m - 5
\][/tex]
From this, we can identify the coefficients [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] as follows:
- [tex]\(A = 8\)[/tex] (the coefficient of [tex]\(m^2\)[/tex])
- [tex]\(B = -4\)[/tex] (the coefficient of [tex]\(m\)[/tex])
- [tex]\(C = -5\)[/tex] (the constant term)
Thus, the values of [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] in that order are:
[tex]\[
\boxed{8 -4 -5}
\][/tex]
