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

Question

.(2 points)
__x^2+___x+___

Answer 1

To multiply the polynomial expressions \( (x + 2)(x - 4) \), 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 perform the multiplication:

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

Now, combine these results:

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

Next, combine like terms \(-4x\) and \(2x\):

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

Thus, the answer can be expressed in the form:

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

Filling in the blanks, we have:

\[ \text{} x^2 + \text{} x + \text{__} \rightarrow 1, -2, -8 \]

So the completed expression is:

1. \(1\)
2. \(-2\)
3. \(-8\)

Final answer: \( x^2 + (-2)x + (-8) \) or \( x^2 - 2x - 8 \).