anonymous
  • anonymous
find all the zeros of the function and write the function as a product of its linear factors. f(x)=3x^4 +2x^3 -28x^2 -14x+56
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
sure you typed it in right?
anonymous
  • anonymous
no lol its f(x)=3x^4 +2x^3-29x^2-14x+56
anonymous
  • anonymous
sorry

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anonymous
  • anonymous
good then cheat http://www.wolframalpha.com/input/?i=+f%28x%29%3D3x^4+%2B2x^3-29x^2-14x%2B56
anonymous
  • anonymous
your supposed to do something else with it...i forgot whats it called but u gotta pull all the number out then find the zeros
anonymous
  • anonymous
zeros are -2, 4/3, and +/- root 7
anonymous
  • anonymous
factor. it is given to you in factored form. once you know -2 is a zero you factor as (x+2) something. you find the something by division
anonymous
  • anonymous
ohh its synthetic divison could do show it by that
anonymous
  • anonymous
i would hate to have to do this by hand.
anonymous
  • anonymous
yes synthetic division list the coefficients. 3 2 -28 -14 56
anonymous
  • anonymous
put a -2 on the side 3 2 -28 -14 56 -2 ______________________________________
anonymous
  • anonymous
no its 3 2 -29 -14 56
anonymous
  • anonymous
where did u get the -2 from the side from?
anonymous
  • anonymous
bring down the three 3 2 -29 -14 56 -2 ______________________________________ 3
anonymous
  • anonymous
no wait wheredid u get the -2 from
anonymous
  • anonymous
3*-2=-6 3 2 -29 -14 56 -2 -6 ______________________________________ 3
anonymous
  • anonymous
i got the -2 because i know -2 is a zero. you have to know that to begin with!
anonymous
  • anonymous
2 + -6 = -4 3 2 -29 -14 56 -2 -6 ______________________________________ 3 -4
anonymous
  • anonymous
wait ok this is what i did i got all the numbers i know what to do i just dont know where u got the -2 from
anonymous
  • anonymous
-4*-2=8 3 2 -29 -14 56 -2 -6 8 ______________________________________ 3 -4
anonymous
  • anonymous
in order to divide i must first know a zero of this function. if i do not i cannot divide. i am dividing by x + 2
anonymous
  • anonymous
why?
anonymous
  • anonymous
-29 + 8 = -21 3 2 -29 -14 56 -2 -6 8 ______________________________________ 3 -4 -21
anonymous
  • anonymous
ok we know that f(-2)=0 so we know f factors as (x+2) q(x) we are trying to find q(x)
anonymous
  • anonymous
we find q(x) by dividing f(x) by x + 2 which is what this synthetic division is doing
anonymous
  • anonymous
if we do not know a zero we do not know what to divide by
anonymous
  • anonymous
i know it is a zero because i cheated and used wolfram alpha. if i had to do it by hand i don't know what i would do. maybe graph it on a calculator and surmise that it crosses the x axis at -2
anonymous
  • anonymous
the factored form of this beast is \[(x+2)(3x-4)(x^2 - 7)\]
anonymous
  • anonymous
i am just factoring out the x + 2 at the moment.
anonymous
  • anonymous
ohh i see
anonymous
  • anonymous
ohh i see
anonymous
  • anonymous
so what are the zeros if it ended with 3 -4 -21 28 0 ?

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