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 polynomial to each term in the second polynomial.

1. Distribute \(x\) from the first polynomial:
\[
x \cdot x + x \cdot (-2) = x^2 - 2x
\]

2. Distribute \(8\) from the first polynomial:
\[
8 \cdot x + 8 \cdot (-2) = 8x - 16
\]

3. Combine all the terms:
\[
x^2 - 2x + 8x - 16
\]

4. Combine like terms (\(-2x + 8x\)):
\[
x^2 + 6x - 16
\]

So, the polynomial can be rewritten as:
\[
x^2 + 6x - 16
\]

Thus, filling in the blanks, we have:
___x^2 + ___x + ___
- First blank: 1
- Second blank: 6
- Third blank: -16

The completed answer is:
___1___x^2 + ___6___x + ___-16___