Question

Which of the following is a polynomial with roots -3, -3i, and 3i ?

x3 + 3x2 + 9x + 27
x3 - 3x2 + 9x - 27
x3 + 9x2 + 9x + 81
x3 - 9x2 + 9x - 81

Answer 1

I got the first one
(x-3i)(x + 3i) = x^2 - 9i^2 = x^2 + 9
(x^2 + 9 )(x + 3) = x^3 + 9x + 3 x^2 + 27 = x^3 + 3 x ^2 + 9 x + 27 = option 1

Answer 2

Ok @JordanGonen First let's ask, what do the factors of -3, -3i, and 3i look like?

If I said the factors of -2 and 4 were (x+2) and (x-4)

What would be your best guess here for the -3, the -3i, and 3i?

Answer 3

-3 = (x+3)
But I have no clue when it comes to the imaginary numbers.
Unless its (x+-3i), which highly doubt.

Answer 4

Right and what is (x+-1) for example?

Answer 5

(x-1) right because we multiply the signs (+) * (-) and this will always be (-) right?

Answer 6

So (x+-3i) is what?

Answer 7

(x-3i)?

Answer 8

It's (x-3i), correct!

Answer 9

so the factor of -3, -3i, and 3i are?

Answer 10

Factors*

Answer 11

(x+3),(x-3i),(x+3i)

Answer 12

Now let's go over a few things about the imaginary number (i)

Great job on showing those factors, those are exactly right.

Answer 13

Do you know what i is equal too?

Answer 14

nope.

Answer 15

We call it imaginary because we cannot take the square root of a negative number.

Answer 16

But (i) is always equal to the sqrt(-1) ok?

Answer 17

Now let me ask this question really quick, do you know how to do this?