To determine which expression is equivalent to the given expression [tex]\( 3(x - 7) + 4(x^2 - 2x + 9) \)[/tex], let's simplify it step-by-step.
We start by distributing and expanding the terms within the expression.
1. Distribute [tex]\(3\)[/tex] in the term [tex]\(3(x - 7)\)[/tex]:
[tex]\[
3(x - 7) = 3x - 21
\][/tex]
2. Distribute [tex]\(4\)[/tex] in the term [tex]\(4(x^2 - 2x + 9)\)[/tex]:
[tex]\[
4(x^2 - 2x + 9) = 4x^2 - 8x + 36
\][/tex]
3. Now, combine these results:
[tex]\[
3x - 21 + 4x^2 - 8x + 36
\][/tex]
4. Combine like terms by bringing together the coefficients of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant terms:
[tex]\[
4x^2 + (3x - 8x) + (-21 + 36)
\][/tex]
5. Simplify the expression further:
[tex]\[
4x^2 - 5x + 15
\][/tex]
Given this simplification, the equivalent expression is:
[tex]\[
4x^2 - 5x + 15
\][/tex]
Therefore, the correct choice from the given options is:
[tex]\[
4x^2 - 5x + 15
\][/tex]
