To find the sum of the given polynomials, let's add the like terms step by step.
Given polynomials:
[tex]\[
\left(8 x^2-9 y^2-4 x\right) \\
\left(x^2-3 y^2-7 x\right)
\][/tex]
First, let's add the [tex]\(x^2\)[/tex] terms:
[tex]\[
8 x^2 + x^2 = 9 x^2
\][/tex]
Next, let's add the [tex]\(y^2\)[/tex] terms:
[tex]\[
-9 y^2 + (-3 y^2) = -9 y^2 - 3 y^2 = -12 y^2
\][/tex]
Finally, let's add the [tex]\(x\)[/tex] terms:
[tex]\[
-4 x + (-7 x) = -4 x - 7 x = -11 x
\][/tex]
Combining these results, we get:
[tex]\[
9 x^2 - 12 y^2 - 11 x
\][/tex]
Therefore, the sum of the polynomials [tex]\((8 x^2-9 y^2-4 x) + (x^2-3 y^2-7 x)\)[/tex] is:
[tex]\[
9 x^2 - 12 y^2 - 11 x
\][/tex]
So, the correct answer is:
[tex]\[
9 x^2 - 12 y^2 - 11 x
\][/tex]
