Let's solve the given expression step-by-step and determine which option matches the simplified form of the expression:
Given expression:
[tex]\[ 3x^2 + 5x - 7(x^2 + 4) \][/tex]
First, let's expand the term [tex]\( -7(x^2 + 4) \)[/tex]:
[tex]\[ -7(x^2 + 4) = -7x^2 - 28 \][/tex]
Now, substitute this back into the original expression:
[tex]\[ 3x^2 + 5x - 7x^2 - 28 \][/tex]
Combine like terms:
[tex]\[ (3x^2 - 7x^2) + 5x - 28 \][/tex]
[tex]\[ -4x^2 + 5x - 28 \][/tex]
So, the simplified expression is:
[tex]\[ -4x^2 + 5x - 28 \][/tex]
Now, we compare this with the given options:
A. [tex]\( x^2 + 28 \)[/tex]
B. [tex]\( -4x^2 + 5x - 28 \)[/tex]
C. [tex]\( x^2 + 4 \)[/tex]
D. [tex]\( -4x^2 + 5x - 4 \)[/tex]
The correct expression that matches our simplified expression [tex]\( -4x^2 + 5x - 28 \)[/tex] is:
B. [tex]\( -4x^2 + 5x - 28 \)[/tex]
Therefore, the correct answer is 2.
