Question

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

Answer 1

To use the Distributive Property to rewrite the polynomial \((x + 8)(x - 2)\), we can expand it as follows:

1. Distribute \(x\) from the first term to both terms in the second polynomial:
\[
x \cdot x + x \cdot (-2) = x^2 - 2x
\]

2. Distribute \(8\) from the first term to both terms in the second polynomial:
\[
8 \cdot x + 8 \cdot (-2) = 8x - 16
\]

3. Now, combine all the terms:
\[
x^2 - 2x + 8x - 16 = x^2 + 6x - 16
\]

So, the final polynomial is:
\[
x^2 + 6x - 16
\]

Filling in the blanks, we have:
- First blank (for \(x^2\)): **1**
- Second blank (for \(x\)): **6**
- Third blank (for the constant): **-16**

So the complete answer is: \(x^2 + 6x - 16\).