Question

the polynomials p(x)=2x^3+kx^2-3x+5 and q(x)= x^3+2x^2-x+k, when divided by (x-2), leave the same remainder (r1) and (r2). find the value of k if (r1)- (r2)=0

Answer 1

from the first equation we get
15+4k=r1
from the second equation we get
14+k=r2
r1-r2=0
r1=r2
therefore
15+4k=14+k
4k-k=14-15
3k=-1
k=-1/3

Answer 2

r1 = 15 + 4k

as,

p(2) = 16 + k(4) - 6 + 5

=15 + 4k.

Hope it helps.