Question

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

Answer 1

To apply the Distributive Property (also known as the FOIL method for binomials), we will expand the polynomial \((x + 8)(x - 2)\).

1. **First**: Multiply the first terms:
\(x \cdot x = x^2\)

2. **Outer**: Multiply the outer terms:
\(x \cdot -2 = -2x\)

3. **Inner**: Multiply the inner terms:
\(8 \cdot x = 8x\)

4. **Last**: Multiply the last terms:
\(8 \cdot -2 = -16\)

Now, combine all of these results:
\[
x^2 - 2x + 8x - 16
\]

Combine the \(x\) terms:
\[
x^2 + (8x - 2x) - 16 = x^2 + 6x - 16
\]

So, the polynomial in the form \(x^2 + bx + c\) is:
\[
x^2 + 6x - 16
\]

Thus, the final result is:
- Fill in the blanks:
- \(b = 6\)
- \(c = -16\)

The completed expression is:
\[
x^2 + 6x - 16
\]