Question

Multiply the polynomial expression (x+2)(x−4)
.(2 points)
x2+
a
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. 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, combine all the results:
\[
x^2 - 4x + 2x - 8
\]

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

So, the final expression is:
\[
x^2 - 2x - 8
\]

In the requested format, the expression can be written as:
\[
x^2 + (-2)x + (-8)
\]

Therefore, \(a = -2\) and the last term is \(-8\).