Let's find the sum of the two given polynomials step-by-step:
Given the polynomials:
[tex]\[ (4x^2 + 6) \][/tex]
and
[tex]\[ (2x^2 + 6x + 3) \][/tex]
Our aim is to add these polynomials together.
1. Identify like terms:
- The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2\)[/tex] from the first polynomial and [tex]\(2x^2\)[/tex] from the second polynomial.
- The [tex]\(x\)[/tex] term: There is no [tex]\(x\)[/tex] term in the first polynomial, and there is [tex]\(6x\)[/tex] in the second polynomial.
- The constant terms: [tex]\(6\)[/tex] from the first polynomial and [tex]\(3\)[/tex] from the second polynomial.
2. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
[tex]\[
4x^2 + 2x^2 = 6x^2
\][/tex]
3. Add the coefficients of the x terms:
[tex]\[
0x + 6x = 6x
\][/tex]
4. Add the constant terms:
[tex]\[
6 + 3 = 9
\][/tex]
Combining all the results, we get the resulting polynomial:
[tex]\[ 6x^2 + 6x + 9 \][/tex]
Thus, the polynomial representing the sum is:
[tex]\[ 6x^2 + 6x + 9 \][/tex]
According to the options given:
A. [tex]\(8x^2 + 6x + 9\)[/tex]
B. [tex]\(8x^2 + 6x + 18\)[/tex]
C. [tex]\(6x^2 + 6x + 9\)[/tex]
D. [tex]\(6x^2 + 6x + 18\)[/tex]
The correct answer is:
C. [tex]\(6x^2 + 6x + 9\)[/tex]
