To find the sum of the given polynomials, you will need to add the corresponding coefficients of each term from both polynomials.
First, let's rewrite the polynomials so that the terms are properly aligned:
1. [tex]\(11x^2 - 5 + x + 4\)[/tex]:
[tex]\[ 11x^2 + 1x - 1 \][/tex]
(This results from combining the constant terms [tex]\(-5\)[/tex] and [tex]\(4\)[/tex] to get [tex]\(-1\)[/tex].)
2. [tex]\(10x^2 - 9\)[/tex]:
[tex]\[ 10x^2 + 0x - 9 \][/tex]
(Here, we have a placeholder for the [tex]\(x\)[/tex] term, which is 0, as the polynomial doesn't have a term with [tex]\(x\)[/tex].)
Now, we add the corresponding coefficients:
- The coefficient of [tex]\(x^2\)[/tex] is:
[tex]\[ 11 + 10 = 21 \][/tex]
- The coefficient of [tex]\(x\)[/tex] is:
[tex]\[ 1 + 0 = 1 \][/tex]
- The constant term (coefficient of [tex]\(x^0\)[/tex]) is:
[tex]\[ -1 + (-9) = -10 \][/tex]
Therefore, the resulting polynomial after summing up the corresponding terms is:
[tex]\[ 21x^2 + 1x - 10 \][/tex]
In summary, the sum of the given polynomials is:
[tex]\[ 21x^2 + 1x - 10 \][/tex]
