To simplify the given expression [tex]\(\left(5x^2 + 3x + 4\right) + \left(2x^2 - 6x + 3\right)\)[/tex], follow these steps:
1. Identify like terms: These are terms that have the same power of [tex]\(x\)[/tex]. In this case, we have:
- [tex]\(5x^2\)[/tex] and [tex]\(2x^2\)[/tex] (these are the quadratic terms)
- [tex]\(3x\)[/tex] and [tex]\(-6x\)[/tex] (these are the linear terms)
- [tex]\(4\)[/tex] and [tex]\(3\)[/tex] (these are the constant terms)
2. Add the coefficients of the quadratic terms:
[tex]\[
5x^2 + 2x^2 = (5 + 2)x^2 = 7x^2
\][/tex]
3. Add the coefficients of the linear terms:
[tex]\[
3x + (-6x) = (3 - 6)x = -3x
\][/tex]
4. Add the constant terms:
[tex]\[
4 + 3 = 7
\][/tex]
5. Combine the results:
[tex]\[
7x^2 - 3x + 7
\][/tex]
So, the simplified polynomial is:
[tex]\[
7x^2 - 3x + 7
\][/tex]
Among the given choices, the correct answer is:
[tex]\[
7 x^2 - 3 x + 7
\][/tex]
