Question

Which of the following is a polynomial with roots -2, -3i, and 3i ?

Answer 1

x3 + 4x2 + 9x + 24
x3 - 4x2 + 9x - 24
x3 + 2x2 + 9x + 18
x3 - 2x2 + 9x - 18

Answer 2

It would be \[Answer=(x+2)(x+3i)(x-3i)\]

Answer 3

how would you solve that?

Answer 4

Multiply the first term by the second term. Then take the product and multiply that with the third and final term.

Answer 5

Use the law of distribution.\[a*(b+c)=(a*b)+(a*c)\]

Answer 6

im confused

Answer 7

Here's a guide for using the FOIL method:

http://www.algebrahelp.com/lessons/simplifying/foilmethod/

Answer 8

i know how to foil

Answer 9

Good! Use the foil method on the first two terms.

Answer 10

Show me what you get.

Answer 11

x^2... im stuck on the x*3i

Answer 12

\[(x+2)(x+3i)=x^{2}+3x i+2x+6i\]

Answer 13

Then multiply that by the last term.

Answer 14

oh.. im dumb

Answer 15

Not at all! We are all here to learn. That's not dumb.

Answer 16

so what do i do form there

Answer 17

\[(x^{2}+3x i+2x+6i)(x-3i)=(x^{2}+3x i+2x+6i)(x)-(x^{2}+3x i+2x+6i)(3i)\]If you look at my generic example of the law of distribution above, 'a' would be that long x squared number.

Answer 18

hmm

Answer 19

these problems suck.. i dont get it

Answer 20

Can you solve (x2+3xi+2x+6i)(x)?

Answer 21

I mean simplify, not solve technically.

Answer 22

3x+4xi+3x+6xi

Answer 23

What's x^2 times x?

Answer 24

x^3

Answer 25

Good. That's the first term. The next term would be 3xi times x.

Answer 26

3i^2

Answer 27

Remember that x and i are different variables representing different numbers. So it would be (3)(x)(i)(x)=3x^2i

Answer 28

oh

Answer 29

Next will be (2x)(x) + (6i)(x)

Answer 30

3x+6xi

Answer 31

(2x)(x)=\[2x^{2}\]

Answer 32

oops

Answer 33

Okay. So what's \[(x^{2}+3x i +2x+6i)(x)=?\]

Answer 34

x^3+3x2i+2x^2+6xi?

Answer 35

Very good. Now do \[(x^{2}+3x i+2x+6i)(3i)\]

Answer 36

3xi^2+6xi^2+6xi+18i^2

Answer 37

Very close. Look at the 3xi times 3i again.

Answer 38

im not sure on that one

Answer 39

You added the three's instead of multiplying them

Answer 40

oh 9xi

Answer 41

\[9x i^{2}\]

Answer 42

my bad

Answer 43

It's okay. I've actually got to get ready for work tmrw. I'm sure someone here will help you finish.

@satellite73
@TuringTest
@ganeshie8

Answer 44

thank you

Answer 45

\[\large (x+2)(x+3i)(x-3i)\]

Answer 46

may be first multiply the last two factors

Answer 47

\[\large (x+2)\color{red}{(x+3i)(x-3i)}\]

Answer 48

recall the identity : \((a+b)(a-b)=a^2-b^2\)

Answer 49

\[\large (x+2)\color{red}{(x^2 - (3i)^2)}\]

Answer 50

umm im kinda lost