Question

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

___x^2 + ___x + ___

Fill in those blanks

Answer 1

To multiply the polynomial expression \((x + 2)(x - 4)\), we can use the distributive property (commonly 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, combining these results:

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

Combine the like terms:

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

So, the final expression is:

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

Now we can fill in the blanks:

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

Thus, the answer is:

1 **x^2 +** (-2) **x +** (-8).