## Christos 2 years ago Factor 15x^2 - 37x + 20

1. hartnn

do you know how to generally factor a quadratic ?

2. Christos

I know some methods but I guess I miss this one

3. hartnn

for \(ax^2+bx+c\), you need to find 2 numbers with sum = b and product = ac so, for your question, you need to find 2 numbers with sum =-37 and product = 20*15 = 300

4. Christos

I see now :)

5. hartnn

so which 2 numbers u get ? then split -37x accordingly...

6. Christos

I got -20 and -15 what now?

7. hartnn

good! split -37x as -20x-15x so, you have \(15x^2-15x-20x+20\) there's a common factor in 1st 2 terms and a common factor in last 2 terms, can you proceed ?

8. hartnn

oh wait, -20 and -15 are incorrect :P

9. Christos

Yea :S

10. hartnn

try another pair ?

11. Christos

-12 -25 ?

12. hartnn

bingo! split -37x as -25x-12x so, you have \(15x^2−25x−12x+20\) there's a common factor in 1st 2 terms and a common factor in last 2 terms, can you proceed ?

13. Christos

x(x15-25)4(3x + 5)

14. hartnn

from first 2 terms factor out 5x

15. Christos

5x(3x - 5) - 4(3x + 20)

16. hartnn

-12x+20 = -4 (3x+.....?)

17. Christos

its 5 sorry

18. hartnn

+5 or -5 ?

19. Christos

-5

20. hartnn

so, now factor 3x-5 from that

21. Christos

What do you mean? I dont understand :SS

22. hartnn

5x (3x-5) -4(3x-5) factor out 3x-5 (3x-5)(5x-4) i meant this, and you're done

Bonjour! Comment allez vous?

24. hartnn

i am fine, do u need any help ? with what ?

You are very good at teaching people

26. hartnn

oh, thank you very much :) :D

27. some_someone

\[15x^2 - 37x + 20 \] \[(3 x-5) (5 x-4)\]