To solve the given expression [tex]\(3(x - 7) + 4(x^2 - 2x + 9)\)[/tex] and determine which of the provided options it is equivalent to, let's break down the expression step by step.
1. Distribute the constants inside the parentheses:
- For [tex]\(3(x - 7)\)[/tex]:
[tex]\[
3(x - 7) = 3x - 21
\][/tex]
- For [tex]\(4(x^2 - 2x + 9)\)[/tex]:
[tex]\[
4(x^2 - 2x + 9) = 4x^2 - 8x + 36
\][/tex]
2. Combine the distributed parts:
[tex]\[
3x - 21 + 4x^2 - 8x + 36
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
4x^2
\][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
3x - 8x = -5x
\][/tex]
- Combine the constant terms:
[tex]\[
-21 + 36 = 15
\][/tex]
4. Write the simplified expression:
[tex]\[
4x^2 - 5x + 15
\][/tex]
Therefore, the expression [tex]\(3(x-7) + 4(x^2 - 2x + 9)\)[/tex] simplifies to [tex]\(4x^2 - 5x + 15\)[/tex].
Thus, the correct answer is:
[tex]\[
4x^2 - 5x + 15
\][/tex]
