You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
function problem
- Thread starter tommy147
- Start date
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
The crucial point is that polynomial f(x) has x- a as a factor if and only if f(a)= 0. Since f(x) has x- 1 as factor, it follows that f(1)= 0. You want to find a value of x such that f(2x-1)= 0. Okay, for what x is 2x- 1= 1?
The crucial point is that polynomial f(x) has x- a as a factor if and only if f(a)= 0. Since f(x) has x- 1 as factor, it follows that f(1)= 0. You want to find a value of x such that f(2x-1)= 0. Okay, for what x is 2x- 1= 1?
i understand that f(1)=0 and f(2x-1)=0, this would be the factor theorem i believe
but the 2x-1=1 part is quite confusing to me
can you explain a little bit on that part? thank you
---edit
after some thought i came up with substituting x=2x-1
then i have
x-1=0
(2x-1)-1=0
2x-1=1
x=0
still confused about how this works though
Last edited:
I at least do not understand the problem. For example, there is no reason to believe that f(2x - 1) has a single factor although you say that you are asked to find "the" factor. Please re-write the problem completely and exactly.i understand that f(1)=0 and f(2x-1)=0, this would be the factor theorem i believe
but the 2x-1=1 part is quite confusing to me
can you explain a little bit on that part? thank you
---edit
after some thought i came up with substituting x=2x-1
then i have
x-1=0
(2x-1)-1=0
2x-1=1
x=0
still confused about how this works though
Sorry about my poor englishI at least do not understand the problem. For example, there is no reason to believe that f(2x - 1) has a single factor although you say that you are asked to find "the" factor. Please re-write the problem completely and exactly.
it should be "a" factor instead of "the" factor
the rest of the problem is correct and no other information is given
I have some clues now but im not very sure about it.
Here are some steps
If x-1 is a factor, then
f(x)=(x-1)Q(x)=0
and x-1=0 or Q(x)=0
assuming x-1=0
for f(2x-1)
it would be
f(2x-1)=((2x-1)-1)Q1(2x-1)
hence, 2x-1-1=0
x=0
from this point onward im stuck..
Here are some steps
If x-1 is a factor, then
f(x)=(x-1)Q(x)=0
and x-1=0 or Q(x)=0
assuming x-1=0
for f(2x-1)
it would be
f(2x-1)=((2x-1)-1)Q1(2x-1)
hence, 2x-1-1=0
x=0
from this point onward im stuck..
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
I think you are just not being careful enough. If 2x- 1= 1 then x is NOT 0! Solve that equation again!
TommyI have some clues now but im not very sure about it.
Here are some steps
If x-1 is a factor, then
f(x)=(x-1)Q(x)=0
and x-1=0 or Q(x)=0
assuming x-1=0
for f(2x-1)
it would be
f(2x-1)=((2x-1)-1)Q1(2x-1)
hence, 2x-1-1=0
x=0
from this point onward im stuck..
As daon explained, the answers provided do not match up with the question provided. I previously explained that the problem provided seems to make no sense. Please make sure that you have copied all parts of the problem exactly. That includes the expressions themselves. I strongly suspect that there is some error in your original statement of the problem.