Question

The polynomial
$ax {}^{3} + bx {}^{2} + x - 6$
has
$(x + 2)$
as a factor and leaves and remainder 4 when divided by
$(x - 2)$
Find a and b

Answer 1

F(x) = ax3 + bx2 + x – 6
F(- 2) = -8a + 4b – 2 – 6 = -8a + 4b – 8 = 0
 So, 2a – b + 2 = 0 ……(i)
F(2) = 8a + 4b + 2 – 6 = 8a + 4b – 4 = 4
 So, 2a + b – 2 = 0 ……..(ii)
  From (i) and (ii), we get
       a = 0 , b = 2,

____________________________

I HOPE THIS ANSWER IS HELP FUL

____________________________