anonymous
  • anonymous
Factor x^3-5x^2-25x+125
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
5x(x^2-x-5+25)
welshfella
  • welshfella
- no - thats gives 5x^3
welshfella
  • welshfella
x+ 5 or x-5 might be a factor find f(5) and see if it = 0

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anonymous
  • anonymous
So (x+5)(x-5)(x-5)
anonymous
  • anonymous
What type of roots of those?
Michele_Laino
  • Michele_Laino
we can factor out x^2 between the first two terms, and we can factor out -25x between the third and the fourth term, so we get this: \[\Large {x^3} - 5{x^2} - 25x + 125 = {x^2}\left( {x - 5} \right) - 25x\left( {x - 5} \right)\]
welshfella
  • welshfella
OOOH - did you guess that?? (x-5) is a factor because f(5) = 0
anonymous
  • anonymous
No. I just did (x^2-25)(x-5)
welshfella
  • welshfella
well you are correct
anonymous
  • anonymous
What type of roots are those?
anonymous
  • anonymous
And thanks youu
Michele_Laino
  • Michele_Laino
oops... we can factor out 25 between the third and the fourth terms, not 25 x: \[\Large {x^3} - 5{x^2} - 25x + 125 = {x^2}\left( {x - 5} \right) - 25\left( {x - 5} \right)\]
welshfella
  • welshfella
right
welshfella
  • welshfella
- you beat me too it!!
anonymous
  • anonymous
So would the roots be -5,-5,5 or -5,5,5?
welshfella
  • welshfella
the roots are 5 and -5 root 5 is a duplicate
anonymous
  • anonymous
Ok but since the polynomial is 3 there has to be 3 roots?
welshfella
  • welshfella
- correction - that was rubbish the roots are 5 , 5 and -5
anonymous
  • anonymous
How?
welshfella
  • welshfella
yes -5 and 5 duplicity 2
welshfella
  • welshfella
factors are (x + 5)(x - 5)(x - 5) the fist gives x = -5 and the other 2 give x = 5
anonymous
  • anonymous
Ohhh<3
anonymous
  • anonymous
Thanks! :)
welshfella
  • welshfella
no 3 roots - because there are 2 5's
welshfella
  • welshfella
the graph will look a bit like |dw:1436970554356:dw|
welshfella
  • welshfella
- just touching the point (5,0)
anonymous
  • anonymous
:) Thank you!!
welshfella
  • welshfella
yw

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