## anonymous 3 years ago Factor 3x⁴-17x³-12x²-62 x+20

1. anonymous

From my calculations, it's unfactorable. Is this a multiple choice answer?

2. anonymous

It's not multiply choice. It is factorable, but into two quadratics. Those cannot be factor. All I'm asking is how do you factor this?

3. anonymous

How do you factor 3x⁴-17x³-12x²-62 x+20 into two quadratics?

4. anonymous

5. anonymous

I get it. I know I have a video of this somewhere. One second.

6. mathslover

Factor theorem will surely work.

7. mathslover

find the factors of 20 first... can you tell me @micahwood50 ?

8. anonymous

I'm not sure how to do this, can you show me?

9. mathslover

what are the factors of 20?

10. anonymous

1, 2, 4, 5, 10, 20

11. mathslover

is -1 , -2 , -4,-5,-10, -20 also factors of 20 ?

12. anonymous

Yeah.

13. mathslover

so , now one by one put : $$\pm 1,\pm 2, \pm 4, \pm 5, \pm 10, \pm 20$$ at the place of x in the given expression

14. mathslover

In which you get the answer as 0 ?

15. mathslover

3x⁴-17x³-12x²-62 x+20 for example : $$3(-1)^4 -17(-1)^3 -12(-1)^2 -62(-1)+20$$ $$-3 +17 -12 + 62 + 20$$ $$84 \ne 0$$ Do like this for each : $$\pm 1,\pm 2, \pm 4, \pm 5, \pm 10, \pm 20$$

16. mathslover

Can you do this @micahwood50 ?

17. anonymous

Umm, I tried all of them, none of them works.

18. anonymous
19. anonymous

those are only the rational roots

20. mathslover

we want integral roots...

21. anonymous

You know what? Save your time and help someone else. I'm googling Factor theorem. Thanks, though.

22. anonymous

if the lowest terms with integer coefficients are quadratics, there aren't any.

23. anonymous

factors, not terms

24. anonymous

that wording was bad, but I think you know what I mean

25. anonymous

$$\large 3x^4-17x^3-12x^2-62x+20 =(3x^2+4x+10)(x^2-7x+2)$$ "Link would be helpful too. " I read a post about factoring into quadratics. Here is a post in which someone tried to explain the method of factoring into quadratics, but I could not understand it. :( http://openstudy.com/users/dpainc#/updates/4fcfdafce4b0c6963adaf2bc

26. anonymous

I don't think that that would apply in this situation, unless you could see that x^2 -7x + 2 is a factor.