To find the sum of the given polynomials, let's add corresponding terms together step by step:
The given polynomials are:
[tex]\[ (8x^2 - 9y^2 - 4x) + (x^2 - 3y^2 - 7x) \][/tex]
We'll add the coefficients of like terms separately:
1. Sum of [tex]\(x^2\)[/tex] terms:
[tex]\[
8x^2 + x^2 = 9x^2
\][/tex]
2. Sum of [tex]\(y^2\)[/tex] terms:
[tex]\[
-9y^2 + (-3y^2) = -9y^2 - 3y^2 = -12y^2
\][/tex]
3. Sum of [tex]\(x\)[/tex] terms:
[tex]\[
-4x + (-7x) = -4x - 7x = -11x
\][/tex]
Now, combine these results to form the sum of the polynomials:
[tex]\[
9x^2 - 12y^2 - 11x
\][/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]
Thus, the correct answer is:
[tex]\[
9 x^2 - 12 y^2 - 11 x
\][/tex]
The correct option is:
[tex]\[
9 x^2 - 12 y^2 - 11 x
\][/tex]
