Question

Multiply the polynomial expression $(x+2)(x-4)$ (2 points)
$\square x^{2}+\square x+\square $

Answer 1

To multiply the polynomial expression \((x+2)(x-4)\), we will use the distributive property (also known as the FOIL method for binomials).

Starting with the expression:

\[
(x+2)(x-4)
\]

We will distribute each term in the first binomial \((x + 2)\) to each term in the second binomial \((x - 4)\):

1. Multiply the first terms:
\[
x \cdot x = x^2
\]

2. Multiply the outer terms:
\[
x \cdot (-4) = -4x
\]

3. Multiply the inner terms:
\[
2 \cdot x = 2x
\]

4. Multiply the last terms:
\[
2 \cdot (-4) = -8
\]

Now, we combine all of these results:

\[
x^2 - 4x + 2x - 8
\]

Next, we combine the like terms \(-4x\) and \(2x\):

\[
-4x + 2x = -2x
\]

Putting it all together, we have:

\[
x^2 - 2x - 8
\]

Thus, the product of the polynomial expression \((x+2)(x-4)\) is:

\[
\boxed{x^2 - 2x - 8}
\]

Filling in the squares as asked:

\(\square x^{2}+\square x+\square\) is \(1\) for \(x^2\), \(-2\) for \(x\), and \(-8\) for the constant.