Question

the polynomial p x = 2 x ki power 4 minus 2 x cube + 3 x square minus A X + b when divided by x minus 1 and X + 1 leave the remainders 5.19 respectively find the values of A and B hence find the remainder between p x is divided by x minus 2​

Answer 1

f(x) = x4 - 2x3 + 3x2 - ax + b

f(1)=5  and  f(-1)=19 ( from given question )

14 - 2.13 + 3.12 - a.1 + b =5  and  (-1)4 - 2(-1)3 + 3(-1)2 - a(-1) + b=19

=> 1-2+3-a+b=5  and  1+2+3+a+b=19

=>2-a+b=5  and  6+a+b=19

=>-a+b=5-2  and  a+b=19-6

=>-a+b=3.....(1)   and  a+b=13....(2)

on subtracting (1) from (2), we get:

a+b-(-a+b)=13-3

a+b+a-b=10

2a=10

a=5

placing a=5 in equation 1, we get,

-5+b=3 , b=8

a=5, b=8 

hope this helps u