## ParthKohli 2 years ago factoring

1. ParthKohli

Should I use $$a^3 + b^3 = (a + b)(a^2 - ab+b^2)$$?

2. ParthKohli

Or am I complicating it?

3. drawar

The factorization is not that easy to find

4. ParthKohli

Yeah, but Wolfram does give a simple solution.

5. drawar

Why simple? Complex numbers join the party and you can't even find a real root to get started...

6. ParthKohli

Yeah, but the solution is simple. :-P This is 9th grade math... I don't know why I'm not able to do this one

7. drawar

Gimme a minute...

8. drawar

$\begin{array}{l} 9{x^4} + 9{x^3} + 8{x^2} + 9x + 9 = 0 \\ 9({x^4} + {x^3} + 2{x^2} + x + 1) = 10{x^2} \\ 9{({x^2} + 1)^2} + 9x({x^2} + 1) - 10{x^2} = 0 \\ {\left( {3({x^2} + 1)} \right)^2} + \left( {3({x^2} + 1)} \right)(3x) - 10{x^2} = 0 \\ {\left( {3({x^2} + 1)} \right)^2} - \left( {3({x^2} + 1)} \right)(2x) + \left( {3({x^2} + 1)} \right)(5x) - (2x)(5x) = 0 \\ \end{array}$ Actually 4 mins already, and I left out the last step :P

9. ParthKohli

Ha, but how did you choose to add $$10x^2$$ to both sides? Doesn't it seem arbitrary?

10. drawar

No it does not. At first glance I was going to add x^2 only, but then to complete the square I have to add another 9x^2

11. ParthKohli

How do you complete the square in a polynomial with degree 3 or higher? :-O

12. ParthKohli

Oh lol

13. ParthKohli

Got it

14. ParthKohli

$(3x)^2 + (3)^2$has the middle term $$2(3x)^2 (3)^2 = 18x^2$$. Thanks :-)

15. drawar

just pick the dominant term with even degree and add/subtract until you have a complete square

16. mathslover

KUDOS FOR DRAWAR , GREAT WORK MR. DRAWAR :)

17. drawar

Thanks for that @mathslover :) Oh kids have to study so many things nowadays...

18. ParthKohli

@drawar Can you send me the link where you learnt how to do this?

19. drawar

Sorry I don't have any link to share here, just do more practice and you'll eventually get the hang of it!

20. ParthKohli

OK :-|

21. drawar

Just out of curiosity, are you a 9th grader?

22. ParthKohli

Yes.

23. ParthKohli

24. drawar

Nice, all the best with your study then!

25. ParthKohli

Thanks!