anonymous
  • anonymous
Which of the following is a factor of f(x) = 5x3 + 24x2 − 75x + 14?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
i tried grouping it didnt work

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welshfella
  • welshfella
yea - i cant see grouping working here
anonymous
  • anonymous
so what would work?
welshfella
  • welshfella
we could try the factor theorem like if f(1) = 0 then x - 1 is a factor but that can be a bit tediuos
anonymous
  • anonymous
x-1 or x+1?
welshfella
  • welshfella
try -1 and 1 but thats no good have you got a list of options?
anonymous
  • anonymous
(x + 1 over 2) (x − 1 over 2) (x + 2) (x − 2)
welshfella
  • welshfella
f(2) = 0 so that makes (x - 20 a factor
welshfella
  • welshfella
* (x - 2)
LynFran
  • LynFran
we can factorize here (x+7)(x-2)(5x-1)
welshfella
  • welshfella
5(8) + 24(2) - 150 + 14 = 0
anonymous
  • anonymous
thanks guys :)
anonymous
  • anonymous
i have another question
welshfella
  • welshfella
you're welcome
anonymous
  • anonymous
will u answer it?
welshfella
  • welshfella
i'll try
anonymous
  • anonymous
Describe the graph of the function f(x) = x3 − 15x2 + 68x − 96. Include the y-intercept, x-intercepts, and the end behavior.
welshfella
  • welshfella
the y-intercept is easy its value of y when x = 0 = 0 - 0 + 0 - 96
anonymous
  • anonymous
so its (0,96)?
welshfella
  • welshfella
you need to factor it to find the x - intercepts
welshfella
  • welshfella
(0 , -96)
anonymous
  • anonymous
ok
anonymous
  • anonymous
and for the x-imtercept?
welshfella
  • welshfella
we can try factoring by look at factors of 96
LynFran
  • LynFran
factor out the function we get (x-3)(x-4)(x-8) now let each bracket equal 0 and solve for x
anonymous
  • anonymous
so x = 3,4 and 8?
welshfella
  • welshfella
2*2*2*2*2*3 (x -3) might be a factor f(3) = 0 so that one - oh LynFran has done it already
anonymous
  • anonymous
so which one of the 3 is my answer?
LynFran
  • LynFran
all 3 are the x intercept
anonymous
  • anonymous
oh
welshfella
  • welshfella
@LynFran = please explain how you got that . Openstudy advises us to guide the poster to the answer
anonymous
  • anonymous
and what is the end point,
LynFran
  • LynFran
https://www.symbolab.com/solver/algebra-calculator/x%5E%7B3%7D-15x%5E%7B2%7D%2B68x-96/?origin=enterkey
anonymous
  • anonymous
how do we find the end point?
anonymous
  • anonymous
how do we find the end point?
welshfella
  • welshfella
lets look at the highest root which is 8 the graph passes through this point (8,0) so we need to look at what hapenns to f(x) for x > 8 find f(9) and f(10) f(9) = 30 f(10) = 84 - the graph is rising towards infinity at the endpoint
anonymous
  • anonymous
so the answer is infinity?
welshfella
  • welshfella
yes
anonymous
  • anonymous
ok thanks man
welshfella
  • welshfella
I was wondering how LynFran was factoring the function so quickly - she was using software to do it for her! Thats no way to learn math - you cant use software in an examination.
welshfella
  • welshfella
yw
anonymous
  • anonymous

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