## anonymous 4 years ago plzz help ... Solve each polynomial equation 1. 15x^3-119x^2-10+16=0 2. x^3-14x^2+47x-18=0 3. 5x^3-27x^2-17x-6=0

1. Mertsj

I notice that these are all cubics. So I would first try to factor by grouping and if that doesn't work, then try synthetic division.

2. anonymous

thank u

3. anonymous

how do i do synthetic division with no divisor or watever its called?

4. Mertsj

Let's look at the first one.. The constant term is 16 and the coefficient of the x^3 term is 15. So the possible rational roots are the factors of 16 over the factors of 15 Use those for your "shelf" numbers in the synthetic division process. If you get a remainder of 0, that number is a root.

5. Mertsj

So the possible rational roots are:$\pm1, \pm2,\pm4,\pm8,\pm16,\pm1/3,\pm1/5,\pm1/15,\pm2/3,\pm4/3,\pm8/3,\pm16/3,\pm2/5,\pm4/5$

6. Mertsj

and so on

7. anonymous

so i take the numbers and do what?

8. Mertsj

|dw:1327020100318:dw|

9. Mertsj

So we see that 8 is a root and (x-8)(15x^2+x-2) are factors.

10. Mertsj

Take the second factor 15x^2+x-2 and use the quadratic formula on it and find the other roots.

11. anonymous

so then the answer is 15x^2-x-2x omg thaks i get it!!!

12. Mertsj

I actually cheated and used a graphing calculator to find the 8

13. anonymous

not 2x sorry

14. Mertsj

No that is not the answer. The 3 answers are 8 and whatever you get when you solve 15x^2+x-2=0

15. anonymous

ohhh so how do i find that out?

16. Mertsj

Don't you know how to solve a quadratic equation with the quadratic formula?

17. anonymous

is that the -b +or - one?

18. Mertsj

yes

19. anonymous

sweet i get it now thank you!!!

20. anonymous

$\left\{5 x^3-119 x^2-10 x+16=0,(x-8) (3 x-1) (5 x+2)=0\right\}\left\{x^3-14 x^2+47 x-18=0,(x-9) \left(x^2-5 x+2\right)=0\right\}\left\{5 x^3-27 x^2-17 x-6=0,(x-6) \left(5 x^2+3 x+1\right)=0\right\}$

21. Mertsj

|dw:1327020932580:dw|

22. anonymous

i got for the first one -1|dw:1327021163596:dw|

23. anonymous

24. Mertsj

Don't you see where I solved it for you?

25. anonymous

oh sorry i wasnt looking .. lol

26. anonymous

i see it now

27. Mertsj

ok

28. anonymous

thanks sooo much

29. Mertsj

yw