Question

factoring

Answer 1

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

Answer 2

Or am I complicating it?

Answer 3

The factorization is not that easy to find

Answer 4

Yeah, but Wolfram does give a simple solution.

Answer 5

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

Answer 6

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

Answer 7

Gimme a minute...

Answer 8

\[\begin{array}{l}
9{x^4} + 9{x^3} + 8{x^2} + 9x + 9 = 0 \\
9({x^4} + {x^3} + 2{x^2} + x + 1) = 10{x^2} \\
9{({x^2} + 1)^2} + 9x({x^2} + 1) - 10{x^2} = 0 \\
{\left( {3({x^2} + 1)} \right)^2} + \left( {3({x^2} + 1)} \right)(3x) - 10{x^2} = 0 \\
{\left( {3({x^2} + 1)} \right)^2} - \left( {3({x^2} + 1)} \right)(2x) + \left( {3({x^2} + 1)} \right)(5x) - (2x)(5x) = 0 \\
\end{array}\]

Actually 4 mins already, and I left out the last step :P

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Oh lol

Answer 13

Got it

Answer 14

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

Answer 15

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

Answer 16

KUDOS FOR DRAWAR , GREAT WORK MR. DRAWAR :)

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

OK :-|

Answer 21

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

Answer 22

Yes.

Answer 23

Just started 9th grade.

Answer 24

Nice, all the best with your study then!

Answer 25

Thanks!