Which of the following is a factor of f(x) = 5x3 + 24x2 − 75x + 14?

- anonymous

Which of the following is a factor of f(x) = 5x3 + 24x2 − 75x + 14?

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- anonymous

@welshfella

- anonymous

@LynFran

- anonymous

i tried grouping it didnt work

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## More answers

- welshfella

yea - i cant see grouping working here

- anonymous

so what would work?

- 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

x-1 or x+1?

- welshfella

try -1 and 1 but thats no good
have you got a list of options?

- anonymous

(x + 1 over 2)
(x − 1 over 2)
(x + 2)
(x − 2)

- welshfella

f(2) = 0
so that makes (x - 20 a factor

- welshfella

* (x - 2)

- LynFran

we can factorize here (x+7)(x-2)(5x-1)

- welshfella

5(8) + 24(2) - 150 + 14 = 0

- anonymous

thanks guys :)

- anonymous

i have another question

- welshfella

you're welcome

- anonymous

will u answer it?

- welshfella

i'll try

- anonymous

Describe the graph of the function f(x) = x3 − 15x2 + 68x − 96. Include the y-intercept, x-intercepts, and the end behavior.

- welshfella

the y-intercept is easy its value of y when x = 0
= 0 - 0 + 0 - 96

- anonymous

so its (0,96)?

- welshfella

you need to factor it to find the x - intercepts

- welshfella

(0 , -96)

- anonymous

ok

- anonymous

and for the x-imtercept?

- welshfella

we can try factoring by look at factors of 96

- LynFran

factor out the function we get (x-3)(x-4)(x-8) now let each bracket equal 0 and solve for x

- anonymous

so x = 3,4 and 8?

- 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

so which one of the 3 is my answer?

- LynFran

all 3 are the x intercept

- anonymous

oh

- welshfella

@LynFran = please explain how you got that . Openstudy advises us to guide the poster to the answer

- anonymous

and what is the end point,

- LynFran

https://www.symbolab.com/solver/algebra-calculator/x%5E%7B3%7D-15x%5E%7B2%7D%2B68x-96/?origin=enterkey

- anonymous

how do we find the end point?

- anonymous

how do we find the end point?

- 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

so the answer is infinity?

- welshfella

yes

- anonymous

ok thanks man

- 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

yw

- anonymous

lol @welshfella

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