## ineedyouubiebs 2 years ago Factor the polynomial: 54k^2-24

1. ineedyouubiebs

@jim_thompson5910 Help?

2. jim_thompson5910

hint: 54k^2 - 24 6(9k^2 - 4)

3. ineedyouubiebs

Where did you get the 9k^2 in the second line?

4. jim_thompson5910

I factored out 6 from the expression

5. jim_thompson5910

54k^2 - 24 6*9k^2 - 6*4 6(9k^2 - 4) .. using the distributive property

6. ineedyouubiebs

@jim_thompson5910 oh okay I get it, but then there's no number that multipies to give -4 and adds to 9? thats where im stuck at

7. jim_thompson5910

from here, you would use the difference of squares rule to factor

8. jim_thompson5910

and 9k^2 - 4 is really 9k^2 + 0k - 4 so you need to find two numbers that multiply to 9*(-4) = -36 and add to 0, then you factor by grouping or you can use the difference of squares rule to factor

9. ineedyouubiebs

the difference of squares rule?

10. jim_thompson5910

difference of squares a^2 - b^2 = (a - b)(a+b)

11. jim_thompson5910

ex: 25x^2 - 49 (5x)^2 - (7)^2 (5x - 7)(5x + 7) So 25x^2 - 49 factors to (5x - 7)(5x + 7)

12. timo86m

|dw:1376179696291:dw|

13. ineedyouubiebs

im sorry im still confuse by this

14. timo86m

basically it has to do with common factors

15. jim_thompson5910

did you see my factoring example with 25x^2 - 49

16. jim_thompson5910

so use that to factor 9k^2 - 4

17. ineedyouubiebs

Following your example so far I've got (3K)^2-(2)^2

18. ineedyouubiebs

@jim_thompson5910

19. jim_thompson5910

keep going

20. ineedyouubiebs

I got (3x-2)(3x-2) ?? @jim_thompson5910

21. jim_thompson5910

close, very close

22. jim_thompson5910

but not quite

23. ineedyouubiebs

where did i go wrong?

24. jim_thompson5910

the difference of squares rule is a^2 - b^2 = (a - b)(a+b)

25. jim_thompson5910

notice how it's minus, then plus (not two minuses)

26. jim_thompson5910

it's NOT a^2 - b^2 = (a - b)(a-b)

27. ineedyouubiebs

so then its (3x-2)(3x+2)

28. jim_thompson5910

good

29. jim_thompson5910