Question

Multiply the polynomial expression (x + 2)(x - 4); Box x ^ 2 + Box x+ Box

Answer 1

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

1. First, distribute \(x\) to both terms in the second polynomial:
- \(x \cdot x = x^2\)
- \(x \cdot (-4) = -4x\)

2. Next, distribute \(2\) to both terms in the second polynomial:
- \(2 \cdot x = 2x\)
- \(2 \cdot (-4) = -8\)

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

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

Now, we can fill in the boxes for the expression \(Box x^2 + Box x + Box\):

- The coefficient of \(x^2\) (which is the first Box) is \(1\).
- The coefficient of \(x\) (which is the second Box) is \(-2\).
- The constant term (which is the third Box) is \(-8\).

Thus, we have:
\[
\text{Box } x^2 + \text{Box } x + \text{Box = } 1x^2 - 2x - 8
\]

Final answer:
- Box 1: \(1\)
- Box 2: \(-2\)
- Box 3: \(-8\)