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

____x^2+____x+____

1 answer

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