Question

Find the two polynomials ax^3+3x^2-9 and 2x^3+4x+a leave the same remainder when divided by x+3

Answer 1

Step-by-step explanation:

When p(x) is divided by (x-2),

By remainder theorem,

Remainder= p(2)

p(2)=a*2^3 + 3*2^2 - 13

       =a*8+3*4-13

      =8a+12-13 = 8a-1

p(2) = 2*2^3-5*2+a

     =2*8-10+a

    =16-10+a = 6+a

Since the remainders of ax^3+3x^2-13 and 2x^3-5x+a are same when divided by x-2,

8a-1 = 6+a

8a-6+a=1

8a+8=1-6=-5

8a=-5-8 =-13

a=-13/8