Write the function f(x)=x^3-2x^2+3x+5 as a polynomial of x-2

Question

jamesj · Answer

Well, it must be third order. So expand it out term by term.  Start with
(x-2)^3 and then see what you have left

i.e., write f(x) = (x-2)^3 + stuff.

Once you've figured out what stuff is, you'll be able to find the coefficient A such that

f(x) = (x-2)^3 + A(x-2)^2 + other stuff

now repeat that step and find the coefficient B such that

f(x) = (x-2)^3 + A(x-2)^2 + B(x-2) + constant

anonymous · Answer

thank again @JamesJ

anonymous · Answer

jamesj is of course correct, but if this is for a calc class you can do this:

$$f(x)=a(x-2)^3+b(x-2)^2+c(x-2)+d$$ 
$$f(2)=d$$ so you can replace $x$ by 2 in the original expression and find $d$ immediately 

then 
$$f'(x)=3a(x-2)^2+2b(x-2)+c$$ and therefore 
$$f'(2)=c$$ replace $x$ by to in derivative of original expression to get $c$

lather, rinse, repeat 

haven't seen @jamesj in a while. where you been?

jamesj · Answer

sat73, how are you?  I've been busy! 

Nice method by the way.

anonymous · Answer

good, and glad you are busy, although we (i at least) missed you here

jamesj · Answer

thanks. I'll drop in now and again, but I have a few things cooking.

anonymous · Answer

great
see you around the pool as they say

jamesj · Answer

that sounds good.  I'll have Mai Tai please!

anonymous · Answer

-.-