Question

Multiply the polynomial expression then fill in the blanks (_)
(x + 2)(x - 4)

_x^2 + _x + _

Answer 1

To multiply the polynomial expression \((x + 2)(x - 4)\), 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 like terms (-4x and 2x):

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

Now we can fill in the blanks as follows:

- The coefficient of \(x^2\) is **1**.
- The coefficient of \(x\) is **-2**.
- The constant term is **-8**.

Therefore, the completed expression is:

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

So the filled blanks are:

1. **1**
2. **-2**
3. **-8**