anonymous
  • anonymous
Factor the polynomial: 54k^2-24
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@jim_thompson5910 Help?
jim_thompson5910
  • jim_thompson5910
hint: 54k^2 - 24 6(9k^2 - 4)
anonymous
  • anonymous
Where did you get the 9k^2 in the second line?

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jim_thompson5910
  • jim_thompson5910
I factored out 6 from the expression
jim_thompson5910
  • jim_thompson5910
54k^2 - 24 6*9k^2 - 6*4 6(9k^2 - 4) .. using the distributive property
anonymous
  • anonymous
@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
jim_thompson5910
  • jim_thompson5910
from here, you would use the difference of squares rule to factor
jim_thompson5910
  • 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
anonymous
  • anonymous
the difference of squares rule?
jim_thompson5910
  • jim_thompson5910
difference of squares a^2 - b^2 = (a - b)(a+b)
jim_thompson5910
  • jim_thompson5910
ex: 25x^2 - 49 (5x)^2 - (7)^2 (5x - 7)(5x + 7) So 25x^2 - 49 factors to (5x - 7)(5x + 7)
anonymous
  • anonymous
|dw:1376179696291:dw|
anonymous
  • anonymous
im sorry im still confuse by this
anonymous
  • anonymous
basically it has to do with common factors
jim_thompson5910
  • jim_thompson5910
did you see my factoring example with 25x^2 - 49
jim_thompson5910
  • jim_thompson5910
so use that to factor 9k^2 - 4
anonymous
  • anonymous
Following your example so far I've got (3K)^2-(2)^2
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
keep going
anonymous
  • anonymous
I got (3x-2)(3x-2) ?? @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
close, very close
jim_thompson5910
  • jim_thompson5910
but not quite
anonymous
  • anonymous
where did i go wrong?
jim_thompson5910
  • jim_thompson5910
the difference of squares rule is a^2 - b^2 = (a - b)(a+b)
jim_thompson5910
  • jim_thompson5910
notice how it's minus, then plus (not two minuses)
jim_thompson5910
  • jim_thompson5910
it's NOT a^2 - b^2 = (a - b)(a-b)
anonymous
  • anonymous
so then its (3x-2)(3x+2)
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
the final answer is 6(3k-2)(3k+2)

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