Question

1. when the expression x^3+ 2kx+2 is divided by x+2, the remainder is less than the remainder when the expression is divided by x+1 find the value of k. help plz​

Answer 1

let the polynomial be

f(x)=x³+2kx+2

is divided by

g(x)=x+2

hence

(x+2) is a factor of f(x)

so comparing with x-a we get a=-2

so

f(a)=0

f(-2)=(-2)³+2*-2*k+2

0=-8-4K+2

4k=-6

K=-6/4

k=-3/2

again

when divided by x+1

g(x)=x+1

hence

x+1 is a factor

so a=-1

f(-1)=-(1)³+2*-1*k+2

0=-1-2k+2

0=1-2k

k=1/2

The value of k is 1/2 when divided by x+1

and

K =-3/2 when divided by x+2