To use the Distributive Property (also known as the FOIL method for binomials) to expand the polynomial \((x+8)(x−2)\), we multiply each term in the first binomial by each term in the second binomial:
- First: \(x \cdot x = x^2\)
- Outer: \(x \cdot (-2) = -2x\)
- Inner: \(8 \cdot x = 8x\)
- Last: \(8 \cdot (-2) = -16\)
Now, we can combine these results:
\[ x^2 - 2x + 8x - 16 \]
Combine the like terms (-2x and 8x):
\[ x^2 + 6x - 16 \]
Thus, the expanded form of \((x+8)(x−2)\) is:
\[ x^2 + 6x - 16 \]
So, the coefficients for the original request are:
- \(1\) for \(x^2\) (the coefficient of \(x^2\))
- \(6\) for \(x\) (the coefficient of \(x\))
- \(-16\) for the constant term
Final answer:
\[ (1)x^2 + (6)x + (-16) \]