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 to rewrite the polynomial \((x + 8)(x - 2)\), we will distribute each term in the first parentheses to each term in the second parentheses.

1. Distribute \(x\) from the first parentheses:
- \(x \cdot x = x^2\)
- \(x \cdot (-2) = -2x\)

2. 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**