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

Question

.(2 points)
_ x2+ _ 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):

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

Calculating each term:

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

Now, combine the like terms:

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

So, the final result is:

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

The completed expression is:

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

Thus, filling in the blanks:

• The coefficient of \(x^2\) is 1,
• The coefficient of \(x\) is -2,
• The constant term is -8,

So, the answer is:

_ 1 _ -2 _ -8