Factoring polynomial

[lmf0610]

please show me step by step to solve
9xcubed + 39xsquared + 12=

 

[Lizzie]

Hi Lisa!

Ok, first, I want you to know that it makes life just a bit easier if you actually write out your equation like this...
9x³ + 39x² + 12 =

In case you don't know how to do this, all you have to do is write 9x then < sup> without the space and then write the number that you want to be up, in this case it's 3, and then end it by writing </ sup> without the space. This makes it look like this : 9x³.

 

[stapel]

To "solve", we need whatever is on the other side of the "equals" sign. Is it "zero", or something else?

Thank you.

Eliz.

 

[soroban]

That cubic has no rational zeros.
. . I'll bet there's a typo . . .


How about: $\displaystyle \;9x^3\,+\,39x^2\,+\,12x\:=\:0$ ?

. . Factor: $\displaystyle \;3x(x^2\,+\,13x\,+\,4)\:=\:0$

. . Factor: $\displaystyle \;3x(x\,+\,4)(3x\,+\,1)\:=\:0$

Therefore: $\displaystyle \;x\,=\,0,\,-4,\,-\frac{1}{3}$

 

[Lizzie]

That would certainly make sense soroban.