A Maths Remainder & Factor Theorem Qn

• POP222

  28 Jan 12, 22:19

  Hey guys! can you help me out with this a maths qn? THANK YOU :)

  Given that when x^2+ax+b and x^2+hx+k are divided by x+p, their remainders are equal. Express p in terms of a,b,h and k. 

   

• frekiwang

  28 Jan 12, 23:23

  By remainder theorem: when x^2+ax+b is divided by x+p, the remainder is (-p)^2+a(-p)+b; when  x^2+hx+k is divided by (x+p), the remainder is (-p)^2+h(-p)+k

  so we have,

  (-p)^2-ap+b=(-p)^2-hp+k

  -ap+hp=k-b

  (a-h)p=(k-b)

  p=(k-b)/(a-h)      (if a<>h)