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

Question

.(2 points)
___x2+___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 these results:

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

Combine like terms:

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

So the final result is:

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

In the requested format:

___x² + ___x + ___

You would fill it in as:

1. 1 (for \(x^2\))
2. -2 (for \(-2x\))
3. -8 (for the constant term)

So the answer is:

1x² - 2x - 8