How do you factor cubics?
Such as x^3+5 x^2+7 x+3
or like
x^3+2 x^2-5 x-6

Thanks,

Question

How do you factor cubics? 
Such as x^3+5 x^2+7 x+3
or  like 
x^3+2 x^2-5 x-6

Thanks,

misty1212 · Answer

HI!!

misty1212 · Answer

$$x^3+5x^2+7x+3$$ and you want to factor it?

sh3lsh · Answer

Yeah!

misty1212 · Answer

if you know one zero then you can factor it
in general they do not factor using integer factors
do you know a zero?

sh3lsh · Answer

Oh okay, so I can guess and check to get the first zero. 
So, I guess and checked that -1 was a factor.

misty1212 · Answer

yes $-1$ is a zero, but as for the factor, if $-1$ is a zero then the factor is $(x+1)$

misty1212 · Answer

that means $$x^3+5x^2+7x+3=(x+1)(\text{some quadratic})$$ which you can find by 
a) long division (ick)
b) synthetic division (very easy) or 
c) thinkin

sh3lsh · Answer

Oh yea! I don't want to make any mistake through c) so I'll pick b! 
I can look at a synthetic division algorithm online! 
Thanks so much!

misty1212 · Answer

if you want to make sure you get it right, just cheat

misty1212 · Answer

http://www.wolframalpha.com/input/?i=x%5E3%2B5x%5E2%2B7x%2B3

misty1212 · Answer

$$\color\magenta\heartsuit
$$

sh3lsh · Answer

Haha! I've got to do this in linear with no calculator so unfortunately, I can't!

sh3lsh · Answer

I have a question in synthetic though,

sh3lsh · Answer

And I resolved it, you're the bomb. Thanks again!