Question

Polynomial 3xcube-5xsquare+kx-2 and -xcube-xsquare+7x+k leave the same remainder when divided by x+2 find value at k

Answer 1

g(x)=x+2, x+2=0, x=-2
f(x)=3x^3-5x^2+kx-2
let f(x)=-2
f(-2)=3(-2)^3-5(-2)^2+k(-2)-2
f(-2)=3*-8-5*4+k*4
f(-2)=-24-20+4k
f(-2)=4+4k

g(x)=x+2,x=-2
f(x)= -x^3-x^2+7x+k
let x =-2
f(-2)=(-2)^3-(-2)^2+7(-2)+k
f(-2)=-8-4-14+k
f(-2)=-12-14+k
f(-2)= -26+k

4+4k= -26+k
4+26=k-4k
30= -3k
30/3=-k
-10=k
value of k = -10

Answer 2

3xcube-5xsquare+kx-2
k=-21