Question

Multiply the polynomial expression (x+2)(x-4)

□x²+□x+□

Answer 1

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

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

Calculating each term, we get:

1. \( x \cdot x = x^2 \)
2. \( x \cdot (-4) = -4x \)
3. \( 2 \cdot x = 2x \)
4. \( 2 \cdot (-4) = -8 \)

Now, we combine these results:

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

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

\[
x^2 + (-4x + 2x) - 8 = x^2 - 2x - 8
\]

So, the final result is:

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

Filling in the blanks, the answer is:

□ \(1\) (coefficient of \(x^2\)),
□ \(-2\) (coefficient of \(x\)),
□ \(-8\) (constant term).

Thus, the complete polynomial is:

\[
1x^2 - 2x - 8
\]