To use the Distributive Property (often referred to as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we will multiply each term in the first binomial by each term in the second binomial:
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First: Multiply the first terms: \[ x \cdot x = x^2 \]
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Outer: Multiply the outer terms: \[ x \cdot (-2) = -2x \]
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Inner: Multiply the inner terms: \[ 8 \cdot x = 8x \]
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Last: Multiply the last terms: \[ 8 \cdot (-2) = -16 \]
Now, combine all these results: \[ x^2 - 2x + 8x - 16 \]
Next, combine the like terms \(-2x\) and \(8x\): \[ x^2 + 6x - 16 \]
So, the rewritten polynomial is: \[ x^2 + 6x - 16 \]
To fill in the blanks: \(x^2 + 6x - 16\) So, the answer is \(1\) (for \(x^2\)), \(6\) (for \(x\)), and \(-16\) (the constant).
Thus, the completed polynomial is: \(x^2 + 6x - 16\)
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