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