## Cutiepo0 Group Title How to factor (x^3 + 1) one year ago one year ago

1. Brittni0605 Group Title

$(x^{3}+1)$

2. Cutiepo0 Group Title

mmhm!

3. bandicoot12 Group Title

no, (x+1)(x^2-x+1)

4. Hero Group Title

$(a + b)^3 = (a + b)(a^2 - ab + b^2)$

5. Brittni0605 Group Title

$(x+1)(x^{2}-x+1)$

6. Hero Group Title

That's the sum of cubes formula I posted above.

7. bandicoot12 Group Title

ya basically what they said

8. Cutiepo0 Group Title

ok but I just established that (x^3+1) and (x+1)^3 weren't the same thing :S

9. Hero Group Title

No, they are not. One is simply x cubed plus one. The other is $$(x + 1) \times (x + 1) \times (x + 1)$$

10. Cutiepo0 Group Title

right, so then how can I use the sum of cubes formula? b/c isn't that for (a+b)3

11. Hero Group Title

Because $$(x^3 + 1) = (x^3 + 1^3)$$

12. Hero Group Title

Remember, $$1 = 1 \times 1 \times 1 = 1^3$$

13. Cutiepo0 Group Title

= (x + 1) ^3 ?? but wouldnt that make it the same??

14. Hero Group Title

No, I just explained to you earlier that $$(x^3 + 1) \ne (x + 1)^3$$

15. Hero Group Title

$$(x^3 + 1) = (x^3 + 1^3)$$ $$(x + 1)^3 = (x + 1)(x + 1)(x + 1)$$

16. Cutiepo0 Group Title

ok, so (a^3 + b^3) doesn't equal (a+b)^3, ever right? Sorry, just trying to wrap my head around it

17. Hero Group Title

The only way is if x = 0 or x = 1

18. Hero Group Title

But in general, they will not be equal

19. Cutiepo0 Group Title

ok, so now though with the sum of cubes formula, the whole point was to find the zeroes of the equation f(x)= (x^3 + 1)(x-17)

20. Cutiepo0 Group Title

and the answer is x=17 and x = -1

21. Cutiepo0 Group Title

so how do I get from the sum of cubes to -1

22. Hero Group Title

Basically, the question is asking: What x values would make $$(x^3 + 1)(x - 17) = 0$$ You know that anything times zero equals zero. So when you expand $$(x^3 + 1)$$ you get $$(x + 1)(x^2 - x + 1)$$ Thus $$(x^3 + 1)(x - 17) = (x + 1)(x^2 - x + 1)(x - 17) = 0$$

23. Hero Group Title

If you look closely you'll realize that if (x + 1) = 0 or if (x - 17) = 0, then the product of the whole thing will be zero. There's only one way to make (x + 1) = 0 There's only one way to make (x - 17) = 0.

24. Hero Group Title

What I say doesn't matter if you don't understand anything.

25. Hero Group Title

The silence is deafening

26. Cutiepo0 Group Title

Oh, I got it, thanks a lot for your help with this :) b/c (x2−x+1) doesn't have any roots, so it's just the other two roots

27. Hero Group Title

Oh goodie :D