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To multiply the polynomial expressions \( (x + 2)(x - 4) \), we can use the distributive property (also known as the FOIL method for binomials):
\[
(x + 2)(x - 4) = x \cdot x + x \cdot (-4) + 2 \cdot x + 2 \cdot (-4)
\]
Calculating each term:
1. \( x \cdot x = x^2 \)
2. \( x \cdot (-4) = -4x \)
3. \( 2 \cdot x = 2x \)
4. \( 2 \cdot (-4) = -8 \)
Now, combine the like terms:
\[
x^2 - 4x + 2x - 8 = x^2 - 2x - 8
\]
So, the final result is:
\[
x^2 - 2x - 8
\]
The completed expression is:
\[
x^2 + (-2)x + (-8)
\]
Thus, filling in the blanks:
- The coefficient of \(x^2\) is 1,
- The coefficient of \(x\) is -2,
- The constant term is -8,
So, the answer is:
\_ 1 \_ -2 \_ -8