To find an equivalent expression for [tex]\( -4x^2 + 2x - 5(1 + x) \)[/tex], we need to simplify it.
### Step-by-Step Simplification:
1. Distribute the -5 through the parentheses:
[tex]\[
-5(1 + x) = -5 \cdot 1 + (-5) \cdot x = -5 - 5x
\][/tex]
2. Substitute the distributed terms back into the original expression:
[tex]\[
-4x^2 + 2x - 5 - 5x
\][/tex]
3. Combine like terms:
[tex]\[
-4x^2 + 2x - 5 - 5x = -4x^2 + (2x - 5x) - 5
\][/tex]
4. Simplify within the parentheses:
[tex]\[
2x - 5x = -3x
\][/tex]
5. Put the simplified terms together:
[tex]\[
-4x^2 - 3x - 5
\][/tex]
So, the simplified expression equivalent to [tex]\( -4x^2 + 2x - 5(1 + x) \)[/tex] is:
[tex]\[
-4x^2 - 3x - 5
\][/tex]
Therefore, the equivalent expression in the given boxes would be completed as:
[tex]\[
\boxed{-4}x^2 + \boxed{-3}x + \boxed{-5}
\][/tex]
