simplify the following polynomial function

Algebra
Tutor: None Selected Time limit: 1 Day

Dec 2nd, 2014

write a,b,c always as cycle order as   ab , bc , ca  , a - b , b- c  , c - a 

P(x) = {- a(x-b)(x-c)/(a-b)(c-a)} +  {- b(x-a)(x-c)/(a-b)(b-c)}  +{- c(x-a)(x-b)/(c-a)(a-b)} , 

   take - sign  common from denominator to get same factors 

= {- a(b-c)(x-b)(x-c) - b(c-a)(x-a)(x-c)- c(a-b)(x-a)(x-b)} /(a-b)(b-c)(c-a)  ,  take lcm 

= {(ca-ab)(x^2-bx-cx+bc)+(ab-bc)(x^2-ax-cx+ca)+(bc-ca)(x^2-ax-bx+ab)}/(a-b)(b-c)(c-a) 

 multiply first 2 & last 2 terms in each term of numerator

={ x^2(ca-ab+ab-bc+bc-ca) +(ca-ab)(-bx-cx)+(ab-bc)(-ax-cx)+(bc-ca)(-ax-bx)+(ca-ab)bc+(ab-bc)ca)+

(bc-ca)ab)}/(a-b)(b-c)(c-a)  , multiply terms of x^2  , x  , constant terms

= {x^2(0) +x(ab^2-ac^2+bc^2-a^2b+a^2c-b^2c)+(abc^2-ab^2c+a^2bc-abc^2+ab^2c-a^2bc)}/(a-b)(b-c)(c-a)

= {0+x(a-b)(b-c)(c-a) +0}/(a-b)(b-c)(c-a) , ab^2-ac^2+bc^2-a^2b+a^2c-b^2c= (a-b)(b-c)(c-a)

= x

if not clear free feel to ask again .

Dec 3rd, 2014

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Dec 2nd, 2014
...
Dec 2nd, 2014
Mar 23rd, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer