Question

Use the Distributive Property to rewrite the polynomial (x+8)(x−2) .(2 points) ( ) x^2+ ( ) x+ ( )

Answer 1

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:

1. **First**: \(x \cdot x = x^2\)
2. **Outer**: \(x \cdot (-2) = -2x\)
3. **Inner**: \(8 \cdot x = 8x\)
4. **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:

\[
(1)x^2 + (6)x + (-16)
\]