Question 22346
you have a long division of {{{v^3 - 6v^2 + 9v - 4}}} by v-4


First thing is do you know how to do long division of numbers? Second thing, can you do it with algebraic expressions?


I cannot really show you the process, set out well here, but i shall try.


Process:
how many times does v (-->from the v-4) go into {{{v^3}}}?. Answer is {{{v^2}}}


Now take this {{{v^2}}} and multiply it by both terms of the v-4 and write the answers under the corresponding terms in the {{{v^3 - 6v^2 + 9v - 4}}}. Now subtract them... You are left with {{{- 2v^2 + 9v - 4}}}


Now repeat the process:
How many times does v (--> from the v-4) go into {{{-2v^2}}}?. Answer is {{{-2v}}}.


Now take this {{{-2v}}} and multiply it by both terms of thet v-4 and write the answers under the correspnding terms in the {{{- 2v^2 + 9v - 4}}}. Now subtract them.. You are left with (v-4).


Now repeat the process:
answer is 1.
blah blah blah... ok?


so, final answer is {{{v^2 - 2v + 1}}}, as stated in your book


jon.