To find the simplified sum of the two polynomials [tex]\(6x^2 + 5x + 2\)[/tex] and [tex]\(4x^2 + 6x + 12\)[/tex], follow these steps:
1. Identify the like terms in each polynomial: Like terms are terms that have the same variable raised to the same power.
- From the first polynomial [tex]\(6x^2 + 5x + 2\)[/tex]:
- [tex]\(6x^2\)[/tex] is the term with [tex]\(x^2\)[/tex],
- [tex]\(5x\)[/tex] is the term with [tex]\(x\)[/tex],
- [tex]\(2\)[/tex] is the constant term.
- From the second polynomial [tex]\(4x^2 + 6x + 12\)[/tex]:
- [tex]\(4x^2\)[/tex] is the term with [tex]\(x^2\)[/tex],
- [tex]\(6x\)[/tex] is the term with [tex]\(x\)[/tex],
- [tex]\(12\)[/tex] is the constant term.
2. Add the coefficients of the like terms:
- For the [tex]\(x^2\)[/tex] terms: Add [tex]\(6x^2\)[/tex] and [tex]\(4x^2\)[/tex]:
[tex]\[
6x^2 + 4x^2 = 10x^2
\][/tex]
- For the [tex]\(x\)[/tex] terms: Add [tex]\(5x\)[/tex] and [tex]\(6x\)[/tex]:
[tex]\[
5x + 6x = 11x
\][/tex]
- For the constant terms: Add [tex]\(2\)[/tex] and [tex]\(12\)[/tex]:
[tex]\[
2 + 12 = 14
\][/tex]
3. Combine the results:
- The simplified sum of the polynomials is:
[tex]\[
10x^2 + 11x + 14
\][/tex]
So, the simplified sum of [tex]\((6x^2 + 5x + 2)\)[/tex] and [tex]\((4x^2 + 6x + 12)\)[/tex] is:
[tex]\[
\boxed{10x^2 + 11x + 14}
\][/tex]
