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

Question

.(2 points)
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):

\[ (x + 2)(x - 4) = x \cdot x + x \cdot (-4) + 2 \cdot x + 2 \cdot (-4) \]

Now, let's calculate each term:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-4) = -4x\)
3. \(2 \cdot x = 2x\)
4. \(2 \cdot (-4) = -8\)

Now, we combine these terms:

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

Combine the like terms \(-4x + 2x\):

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

Thus, the expression \((x+2)(x-4)\) simplifies to:

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

To answer your question:

The completed polynomial is: \[ x^2 - 2x - 8 \]

So, filling in the blanks:

• The term for \(x^2\) is \(x^2\).
• The term for \(x\) is \(-2\).
• The constant term is \(-8\).

In your format: \(x^2 + x + (-8)\). The final polynomial is:

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