Question

If the polynomials ( k x cube + 3x square - 13 ) and ( 5x cube - 8x + k ) leave the same remainder when divided by x+1, then find the value of k.

Answer 1

let ,
p(x)=kx^3+3x^2-13

and

g(x)=5x^3-8x+k


x+1=0
x=-1      

both p(x) and g(x) when divided by x+1 leaves the same remainder so/ p(x)=g(x)
now, x=-1
so,    p(-1)=g(-1)

=k(-1)^3+3(-1)^2-13  =  5(-1)^3-8(-1)+k
=-k+3-13=-5+8+k
=-k-10=3+k
=-10-3=k+k
=-13=2k
=k=13/2