Question

if 2x^3+ax^2+bx-2 has a factor(x-1) and leaves a remainder 2
when divided by x-2,find the values of a and b.With these values of a and b,factorise the given polynomial completely.

Answer 1

p(x) = 2x^3 + ax^2 +bx -2

x-1 = 0.   x = 1

p(1)= 2 + a + b - 2 =0

a+b = 0 ------------------------ equ.1

now, x = 2

p(2) = 16 + 4a + 2b -2 = 2

4a + 2b = -12

2a + b = -6---------------------------- equ.2

equ.2 - equ.1

2a + b -a -b = -6-0

a = -6

from equ.1,  b = -a

b = -(-6)

   = 6

p(x) = 2x^3 - 6x^2 + 6x - 2