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How to express $2x-1$ in the form $x-a$ ? Isn't $x-1/2$ wrong?

And how to express $2x+3$ in the form x-a?

this is for using it in the remainder theorem:

when $f(x)$ is divided by $x-a$, the remainder is $f(a)$

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    I'm afraid that $2x-1=2(x-\frac12)$ is the best you can do.2011-07-23
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    $2x-1=2\left(x-\frac{1}{2}\right)$. What exactly you want to get?2011-07-23
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    remainder theorem $x-a$2011-07-23
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    It seems that you are trying to have all the coefficient as integers, which is something that is not always possible.2011-07-23
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    @Asaf Probably the OP is working with polynomials over a field, e.g. the coefficient ring may be $\:\mathbb Q,\:\mathbb R\:$ or $\:\mathbb C\:.\:$2011-07-23
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    @Bill: Yes, this is my point. Many times students expect "pretty" numbers (i.e. integers) but often (in mathematics) this is not the case.2011-07-23
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    @Asaf Huh? Over a field there is no problem. I see nothing in the question to indicate that the OP might be working in $\rm\:\mathbb Z[x]\:.$ It seems to me that the OP is simply asking how to transform the general linear polynomial to the form $\rm\ x-a\ $ so that it matches the (monic) form of the Remainder Theorem known by the OP.2011-07-23

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