To use the Distributive Property to rewrite the polynomial \((x + 8)(x - 2)\), we will distribute each term in the first parentheses to each term in the second parentheses.
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Distribute \(x\) from the first parentheses:
- \(x \cdot x = x^2\)
- \(x \cdot (-2) = -2x\)
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Distribute \(8\) from the first parentheses:
- \(8 \cdot x = 8x\)
- \(8 \cdot (-2) = -16\)
Now, combine all the results: \[ x^2 - 2x + 8x - 16 \]
Next, combine like terms \(-2x + 8x\): \[ x^2 + 6x - 16 \]
So, filling in the blanks:
- The coefficient of \(x^2\) is 1.
- The coefficient of \(x\) is 6.
- The constant term is -16.
The rewritten polynomial is: \[ 1x^2 + 6x - 16 \]
So, the final answer is: 1, 6, -16