Ihave no idea how to do this. i can’t cooperate with the imaginary number, me

Step-by-step explanation:

This is a third degree polynomial because we are given three roots to multiply together to get it.  Even though we only see "2 + i" the conjugate rule tells us that 2 - i MUST also be a root.  Thus, the 3 roots are x = -4, x = 2 + i, x = 2 - i.

Setting those up as factors looks like this (keep in mind that the standard form for the imaginary unit in factor form is ALWAYS "x -"):

If x = -4, then the factor is (x + 4)

If x = 2 + i, then the factor is (x - (2 + i)) which simplifies to (x - 2 - i)

If x = 2 - i, then the factor is (x - (2 - i)) which simplifies to (x - 2 + i)

Now we can FOIL all three of those together, starting with the 2 imaginary factors first (it's just easier that way!):

(x - 2 - i)(x - 2 + i) =

Combining like terms and canceling out the things that cancel out leaves us with:

Remembr that , so we can rewrite that as

and

That's the product of the 2 imaginary factors.  Now we need to FOIL in the real factor:

That product is

which simplifies down to

And there you go!

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.