Question

find the complex zeros of the polynomial function. write f in factored form f(x)=x^4+12x^2+11

Answer 1

try thinking about it like
how would you have factored x^2 + 12x + 11 ?

Answer 2

do you put the like terms together

Answer 3

mmm I don't see how there are like terms?

Answer 4

yeah i hate math so im confused

Answer 5

factor x^2 + 12x + 11 do you know how to do that?

Answer 6

no

Answer 7

well how about like this
x^2 + 6x + 5 = (x + 5)(x+1)
because 5+1=6 (the middle term)
and 5*1=5 (the third term)

Answer 8

so it would be (x+11)(x+1)

Answer 9

yep! :)

then x^4 + 12x^2 + 11 is the same idea
just replace x with x^2 in the factored form :)


like x^4 + 6x^2 + 5 = (x^2 + 5)(x^2 + 1)

Answer 10

ok so x^4+12x^2+11=(x^4+12)(x^4+11)

Answer 11

mmm not quite :)
x^4 + 6x^2 + 5 = (x^2 + 5)(x^2 + 1)
^ left with x^2 not x^4

Answer 12

so its (x^2+12)(x^2+11)
yeah now im confused why is it ^2 and not ^4

Answer 13

(x^2 + 11)(x^2+1)
because when you FOIL it (distribute it out)
you would get
(x^2)(x^2) + 11x^2 + 1x^2 + (1)(11) which simplifies to
x^4 + 12x^2 + 11

Answer 14

okay no i get it we are using the FOIL method

Answer 15

so in factored form would be (x^2)(x^2) + 11x^2 + 1x^2 + (1)(11)

Answer 16

mmm that would be the factored form distributed
factored form would be (x^2+11)(x^2+1)

Answer 17

ok

Answer 18

so this is factored form using complex zeros (x^2+11)(x^2+1)

Answer 19

then to find the complex zeros
find x for each when
x^2+11=0 and x^2+1=0

Answer 20

ok so f(x)=

Answer 21

http://www.wolframalpha.com/input/?i=0%3Dx%5E4%2B12x%5E2%2B11

Answer 22

okay they gave me f(x)=(x^2+1)(x^2+11)

Answer 23

hmm?

Answer 24

is it wrong

Answer 25

no?

Answer 26

yes whats the question

Answer 27

write f in factored form f(x)=x^4+12x^2+11
would be f(x)=(x^2+1)(x^2+11)

then the other half of the question
find the complex zeros of the polynomial function.
would be find x for each when
x^2+11=0 and x^2+1=0

Answer 28

then it says use the complex zeros to write f in factor form

Answer 29

mmm then yeah, factored form is f(x)=(x^2+1)(x^2+11)

Answer 30

ok