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

- anonymous

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- anonymous

sure you typed it in right?

- anonymous

no lol its f(x)=3x^4 +2x^3-29x^2-14x+56

- anonymous

sorry

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## More answers

- anonymous

good then cheat
http://www.wolframalpha.com/input/?i=+f%28x%29%3D3x^4+%2B2x^3-29x^2-14x%2B56

- 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

zeros are -2, 4/3, and +/- root 7

- 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

ohh its synthetic divison could do show it by that

- anonymous

i would hate to have to do this by hand.

- anonymous

yes synthetic division
list the coefficients.
3 2 -28 -14 56

- anonymous

put a -2 on the side
3 2 -28 -14 56
-2
______________________________________

- anonymous

no its 3 2 -29 -14 56

- anonymous

where did u get the -2 from the side from?

- anonymous

bring down the three
3 2 -29 -14 56
-2
______________________________________
3

- anonymous

no wait wheredid u get the -2 from

- anonymous

3*-2=-6
3 2 -29 -14 56
-2
-6
______________________________________
3

- anonymous

i got the -2 because i know -2 is a zero. you have to know that to begin with!

- anonymous

2 + -6 = -4
3 2 -29 -14 56
-2
-6
______________________________________
3 -4

- 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

-4*-2=8
3 2 -29 -14 56
-2
-6 8
______________________________________
3 -4

- 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

why?

- anonymous

-29 + 8 = -21
3 2 -29 -14 56
-2
-6 8
______________________________________
3 -4 -21

- 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

we find q(x) by dividing f(x) by x + 2 which is what this synthetic division is doing

- anonymous

if we do not know a zero we do not know what to divide by

- 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

the factored form of this beast is
\[(x+2)(3x-4)(x^2 - 7)\]

- anonymous

i am just factoring out the x + 2 at the moment.

- anonymous

ohh i see

- anonymous

ohh i see

- anonymous

so what are the zeros if it ended with 3 -4 -21 28 0 ?

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