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

Question

.(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: \[ x^2 + 6x - 16 \]