Question

Find the complex zeros of the polynomial functions. Write f in factored form
a. f(x)=x^3-216
b. f(x)=x^3-4x^2+14x-20
c. x^4+6x^2+5

**Use the complex zeros to write f in factored form

Answer 1

@jim_thompson5910 Could you help me with this problem please?

Answer 2

x^3-216 can be factored using a difference of cubes

x^3-216 = x^3 - 6^3 = (x-6)(x^2 + 6*x + 6^2) = (x-6)(x^2 + 6x + 36)

the others will have to use a graphing calculator

Answer 3

actually with part c), you can let z = x^2 which means z^2 = x^4

Answer 4

it says (x-6)(x^2+6x+36) is wrong

Answer 5

oh you have to solve x^2+6x+36 = 0 now

Answer 6

oh okay gotcha

Answer 7

to get the complex roots

Answer 8

what am i supposed to get for the complex roots,cause it says im wrong again

Answer 9

what did you get when you solved x^2+6x+36 = 0

Answer 10

btw this problem

http://assets.openstudy.com/updates/attachments/5459ba7ee4b07e447429d065-mhm120-1415167239637-4.69.png

is different from what you originally posted

Answer 11

yeah i know sorry i accidentally posted that one

Answer 12

and i got
3(-1-i\[3(-1-\sqrt{3}) and 3(-1+i \sqrt{3})\]

Answer 13

sorry ignore the first part the "3(-1-i" part

Answer 14

so x^2+6x+36 factors to

\[\Large (x-3(-1-i\sqrt{3}))(x-3(-1+i\sqrt{3}))\]

it might be easier to write it like this

\[\Large (x+3+3i\sqrt{3})(x+3-3i\sqrt{3})\]

this is just for the x^2+6x+36 portion though

Answer 15

so it's be (x-6) (x+3+3i√3)(x+3−3i√3) ??

Answer 16

idk what happened there one second

Answer 17

yeah correct

Answer 18

\[(x-6)(x+3+3i \sqrt{3})(x+3-3i \sqrt{3})\]

Answer 19

oh okay thanks!!

Answer 20

np

Answer 21

how do you do part c again , i don't understand the z^2=x^4

Answer 22

Let z = x^2

square both sides to get z^2 = x^4

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the expression

x^4+6x^2+5

turns into

z^2+6z+5

after you do substitutions

Answer 23

now factor z^2+6z+5 to get ???

Answer 24

(z+3)(z+2)

Answer 25

now that you know (z+3)(z+2), you would replace each z with x^2

(z+3)(z+2)

(x^2+3)(x^2+2)

Answer 26

you can factor each further, but you'll get complex factors

Answer 27

o i would get \[(-i \sqrt{3}) and (i \sqrt{3})\]

Answer 28

for x^2+3, yes

Answer 29

that means x^2+3 factors to

\[\Large (x - i\sqrt{3})(x + i\sqrt{3})\]