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

.(2 points)
_ x2+ _ x+ _

1 answer

To multiply the polynomial expressions (x+2)(x4), we can use the distributive property (also known as the FOIL method for binomials):

(x+2)(x4)=xx+x(4)+2x+2(4)

Calculating each term:

  1. xx=x2
  2. x(4)=4x
  3. 2x=2x
  4. 2(4)=8

Now, combine the like terms:

x24x+2x8=x22x8

So, the final result is:

x22x8

The completed expression is:

x2+(2)x+(8)

Thus, filling in the blanks:

  • The coefficient of x2 is 1,
  • The coefficient of x is -2,
  • The constant term is -8,

So, the answer is:

_ 1 _ -2 _ -8