## animalsavior94 4 years ago 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

1. satellite73

sure you typed it in right?

2. animalsavior94

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

3. animalsavior94

sorry

4. satellite73
5. animalsavior94

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

6. satellite73

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

7. satellite73

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

8. animalsavior94

ohh its synthetic divison could do show it by that

9. satellite73

i would hate to have to do this by hand.

10. satellite73

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

11. satellite73

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

12. animalsavior94

no its 3 2 -29 -14 56

13. animalsavior94

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

14. satellite73

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

15. animalsavior94

no wait wheredid u get the -2 from

16. satellite73

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

17. satellite73

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

18. satellite73

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

19. animalsavior94

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

20. satellite73

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

21. satellite73

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

22. animalsavior94

why?

23. satellite73

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

24. satellite73

ok we know that f(-2)=0 so we know f factors as (x+2) q(x) we are trying to find q(x)

25. satellite73

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

26. satellite73

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

27. satellite73

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

28. satellite73

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

29. satellite73

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

30. animalsavior94

ohh i see

31. animalsavior94

ohh i see

32. animalsavior94

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