Question

14. The polynomial p(x) = x ^4- 2x ^3+ 3x^2-ax+b when divided by (x - 1) and
(x + 1) leaves the remainders 5 and 19 respectively. Find the values of a
and b. Hence, find the remainder when p(x) is divided by (x-2)​

Answer 1

Answer:

Step-by-step explanation:

x-1 = 0                                   x+1 = 0      

x = 1                                        x = -1

putting value of x                  putting value of x

1-8+9-a+b = 5                         1+8+9+a+b = 19

2-a+b = 5                                18+a+b = 19

1. b-a = 3                                  2.a+b = 1

adding 1,2

2b = 4                                            

b = 2

2-a = 3                                       a = -1

a = -1                                          b = 2