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!

step-by-step explanation:

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step-by-step explanation:

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