Question

if two polynomials ax³ + 4x² + 3x - 4 and x³ - 4x + a leave the same remainder when divided by x - 3, find the value of a

Answer 1

Answer:

p(x)= ax³+4x²+3x-4

p(3) =a*3³+4*3²+3*3-4

        = 27a+36+9-4

        ⇒ 27a+41

now,

g(x) = x³-4x+a

g(3) = 3³-4*3+a

       = 27-12+a

       = 15+a

both the polynomials leave same remainder

∴ 27a+41 = 15+a

  27a-a = 15-41

  26a = -26

  a = -1