Sure, let's go through the process of simplifying the given expression step by step.
We need to simplify:
[tex]\[ \left(3x^2 - 4x + 6\right) + \left(7x - 2\right) \][/tex]
Step 1: Remove the parentheses and write all the terms together.
[tex]\[ 3x^2 - 4x + 6 + 7x - 2 \][/tex]
Step 2: Combine like terms. Like terms are terms that have the same variable raised to the same power.
First, let's handle the [tex]\(x^2\)[/tex] terms:
[tex]\[ 3x^2 \][/tex]
Next, combine the [tex]\(x\)[/tex] terms:
[tex]\[ -4x + 7x = 3x \][/tex]
Finally, combine the constant terms:
[tex]\[ 6 - 2 = 4 \][/tex]
Step 3: Now, putting it all together, we get:
[tex]\[ 3x^2 + 3x + 4 \][/tex]
So, the simplified expression is:
[tex]\[ 3x^2 + 3x + 4 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
The correct choice is B: [tex]\( 3x^2 + 3x + 4 \)[/tex].
