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, we get:
- \( x \cdot x = x^2 \)
- \( x \cdot (-4) = -4x \)
- \( 2 \cdot x = 2x \)
- \( 2 \cdot (-4) = -8 \)
Now, we combine these results:
\[ x^2 - 4x + 2x - 8 \]
Next, combine the like terms \(-4x\) and \(2x\):
\[ x^2 + (-4x + 2x) - 8 = x^2 - 2x - 8 \]
So, the final result is:
\[ x^2 - 2x - 8 \]
Filling in the blanks, the answer is:
□ \(1\) (coefficient of \(x^2\)), □ \(-2\) (coefficient of \(x\)), □ \(-8\) (constant term).
Thus, the complete polynomial is:
\[ 1x^2 - 2x - 8 \]