Question

Which of the following is a polynomial with roots:

Answer 1

\[2, -2i , 2i\]

Answer 2

the one that looks like
\[(x-2)(x+2i)(x-2i)\]

Answer 3

or what you get when you multiply this out, which is not as hard as it seems since
\[(x+2i)(x-2i)=x^2+4\]so your real job is to multiply
\[(x-2)(x^2+4)\]

Answer 4

-5

Answer 5

except.. these are what I can choose from for this question: x3 – 4x2 + 4x – 16

x3 + 4x2 + 4x + 16

x3 + 2x2 + 4x + 8

x3 – 2x2 + 4x – 8

Answer 6

there is no -5 in the problem
multiply
\[(x-2)(x^2+4)\] and see which one you get

Answer 7

..I got -5?..

Answer 8

\[(x-2)(x^2+4)\] is a polynomial, not a number

Answer 9

i.e. multiply out using the distributive law. sometimes known by the unfortunate acronym "foil"

Answer 10

im confused. I do not understand

Answer 11

your job is to find a polynomial with three zeros, namely \(2,-2i,2i\)
the way you can find this polynomial is first write it in factored form, as
\[(x-2)(x+2i)(x-2i)\]

just like if you were going to solve \(x^2-3x+2=0\) you would write in factored form as \((x-1)(x-2)=0\)

in this case you know the zeros, so you know how to factor
your job here is to multiply out
just like if you multiply \((x-1)(x-2)\) you get \((x-1)(x-2)=x^2-3x-2\)

Answer 12

therefore what you need to do to solve is this problem is to multiply three factors together
you must multiply \((x-2)(x+2i)(x-2i)\)

Answer 13

first you multiply the two terms \((x+2i)(x-2i) =x^2+4\) and then you multiply
\[(x-2)(x^2+4)\] and see which if the three answers above you get

Answer 14

it is clear how to multiply these two terms together?