## sh3lsh one year ago 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,

1. misty1212

HI!!

2. misty1212

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

3. sh3lsh

Yeah!

4. misty1212

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

5. sh3lsh

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

6. misty1212

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

7. misty1212

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

8. sh3lsh

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!

9. misty1212

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

10. misty1212
11. misty1212

$\color\magenta\heartsuit$

12. sh3lsh

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

13. sh3lsh

I have a question in synthetic though,

14. sh3lsh

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