Question

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

Answer 1

@welshfella

Answer 2

@LynFran

Answer 3

i tried grouping it didnt work

Answer 4

yea - i cant see grouping working here

Answer 5

so what would work?

Answer 6

we could try the factor theorem

like if f(1) = 0 then x - 1 is a factor
but that can be a bit tediuos

Answer 7

x-1 or x+1?

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

* (x - 2)

Answer 12

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

Answer 13

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

Answer 14

thanks guys :)

Answer 15

i have another question

Answer 16

you're welcome

Answer 17

will u answer it?

Answer 18

i'll try

Answer 19

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

Answer 20

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

Answer 21

so its (0,96)?

Answer 22

you need to factor it to find the x - intercepts

Answer 23

(0 , -96)

Answer 24

ok

Answer 25

and for the x-imtercept?

Answer 26

we can try factoring by look at factors of 96

Answer 27

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

Answer 28

so x = 3,4 and 8?

Answer 29

2*2*2*2*2*3

(x -3) might be a factor
f(3) = 0
so that one

- oh LynFran has done it already

Answer 30

so which one of the 3 is my answer?

Answer 31

all 3 are the x intercept

Answer 32

oh

Answer 33

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

Answer 34

and what is the end point,

Answer 35

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

Answer 36

how do we find the end point?

Answer 37

how do we find the end point?

Answer 38

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

Answer 39

so the answer is infinity?

Answer 40

yes

Answer 41

ok thanks man

Answer 42

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.

Answer 43

yw

Answer 44

lol @welshfella