Question

Find a and b so the the polynomial x^4+ax^3-7x^2+8x+b is exactly divisible by X^2+5x+6

Answer 1

x2 + 5 x + 6  has  x + 2  as  one  factor,  hence

if  we  put  x = -2, value  of P( X ) should  be  zero, so

16 - 8a - 28 - 16 + b = 0  or  b - 8a = 28. so  if a = 1 then b = 36