Question

the polynomial p(x) =
$2x {}^{3} + kx {}^{2} - {3}x + 5$
And q(x) =
${x}^{3} + 2x {}^{2} - x + k$
Leave the remainder r1 and r2 when divided by x-2 respectively. Find k if r1-r2=0

Answer 1

substitute x=2 in first equation 15+4k=r1 . substitute x=2 in second eqn 18+k=r2. Since r1=r2 k=1.