Let's find the sum of the polynomials [tex]\(-x^2 + 9\)[/tex] and [tex]\(-3x^2 - 11x + 4\)[/tex].
1. Combine the [tex]\(x^2\)[/tex] terms:
- The first polynomial [tex]\(-x^2 + 9\)[/tex] has a term [tex]\(-x^2\)[/tex].
- The second polynomial [tex]\(-3x^2 - 11x + 4\)[/tex] has a term [tex]\(-3x^2\)[/tex].
Adding these terms together:
[tex]\[
-x^2 + (-3x^2) = -4x^2
\][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
- The first polynomial [tex]\(-x^2 + 9\)[/tex] has no [tex]\(x\)[/tex] term (which is the same as having [tex]\(0 \cdot x\)[/tex]).
- The second polynomial [tex]\(-3x^2 - 11x + 4\)[/tex] has a term [tex]\(-11x\)[/tex].
Adding these terms together:
[tex]\[
0x + (-11x) = -11x
\][/tex]
3. Combine the constant terms:
- The first polynomial [tex]\(-x^2 + 9\)[/tex] has a constant term [tex]\(9\)[/tex].
- The second polynomial [tex]\(-3x^2 - 11x + 4\)[/tex] has a constant term [tex]\(4\)[/tex].
Adding these terms together:
[tex]\[
9 + 4 = 13
\][/tex]
So, the sum of the polynomials [tex]\(-x^2 + 9\)[/tex] and [tex]\(-3x^2 - 11x + 4\)[/tex] is:
[tex]\[
-4x^2 - 11x + 13
\][/tex]
The correct answer is:
[tex]\[
-4 x^2 - 11 x + 13
\][/tex]
