Question

Multiply the polynominal expression (x + 2)(x - 4)
?x^2 + ?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):

1. **First**: Multiply the first terms:
\( x \cdot x = x^2 \)

2. **Outer**: Multiply the outer terms:
\( x \cdot (-4) = -4x \)

3. **Inner**: Multiply the inner terms:
\( 2 \cdot x = 2x \)

4. **Last**: Multiply the last terms:
\( 2 \cdot (-4) = -8 \)

Now, combine all the results:
\[
x^2 - 4x + 2x - 8
\]

Combine the like terms (\(-4x + 2x\)):
\[
x^2 - 2x - 8
\]

Thus, the final result is:
\[
x^2 - 2x - 8
\]

In summary, the coefficients are:
\(? = 1\),
\(? = -2\),
\(? = -8\)

So the polynomial expression is \( x^2 - 2x - 8 \).

Answer 2

Make it fit the boxes

Answer 3

Sure! Based on the expression we derived from multiplying the polynomials \((x + 2)(x - 4)\), we have:

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

Now, let's fill in the boxes accordingly:

- For \( x^2 \): **1** (coefficient of \(x^2\))
- For \( x \): **-2** (coefficient of \(x\))
- For the constant term: **-8**

So the answers to fit the boxes would be:

- ? (for \(x^2\)): **1**
- ? (for \(x\)): **-2**
- ? (for the constant term): **-8**