Question

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

__x^2 +__x + __

Answer 1

To use the Distributive Property (often referred to as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we will multiply each term in the first binomial by each term in the second binomial:

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 these results:
\[
x^2 - 2x + 8x - 16
\]

Next, combine the like terms \(-2x\) and \(8x\):
\[
x^2 + 6x - 16
\]

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

To fill in the blanks:
___\(x^2 + 6x - 16\)___
So, the answer is \(1\) (for \(x^2\)), \(6\) (for \(x\)), and \(-16\) (the constant).

Thus, the completed polynomial is:
\(x^2 + 6x - 16\)