To find the sum of the two given polynomials, we need to identify and combine the coefficients of the like terms. The polynomials given are:
1) [tex]\( 11x^2 - 5 \)[/tex]
2) [tex]\( x + 4 \)[/tex]
To sum these polynomials, follow these steps:
1. Identify Like Terms:
- Terms with [tex]\(x^2\)[/tex]: [tex]\(11x^2\)[/tex] from the first polynomial.
- Terms with [tex]\(x\)[/tex]: [tex]\(x\)[/tex] from the second polynomial.
- Constant terms: [tex]\(-5\)[/tex] from the first polynomial and [tex]\(4\)[/tex] from the second polynomial.
2. Sum the Coefficients of Like Terms:
- For [tex]\(x^2\)[/tex]: There is only one [tex]\(x^2\)[/tex] term which is [tex]\(11x^2\)[/tex].
- For [tex]\(x\)[/tex]: There is one [tex]\(x\)[/tex] term which is [tex]\(x\)[/tex], and no [tex]\(x\)[/tex] term in the first polynomial. So, the sum is [tex]\(x\)[/tex].
- For the constants: Combine [tex]\(-5\)[/tex] and [tex]\(4\)[/tex].
[tex]\[ 11x^2 + x + (-5 + 4) \][/tex]
3. Simplify the Constant Term:
[tex]\[ -5 + 4 = -1 \][/tex]
4. Combine the Results:
Thus, the sum of the polynomials is:
[tex]\[ 11x^2 + x - 1 \][/tex]
So the correct answer is:
[tex]\[ 11 x^2 + x - 1 \][/tex]
