F4 maths 續多項式----因式定理

1a)
已知先岩
f(x)=8x^3+(4k+4)x^2-4x+k
若f(x)可被2x+k整除,f(-k/2)=0
f(-k/2)=8(-k/2)^3+(4k+4)(-k/2)^2-4(-k/2)+k=0
f(-k/2)=-k^3+(k+1)k^2+2k+k=0
f(-k/2)=-k^3+k^3+k^2+3k=0
f(-k/2)=k^2+3k=0
f(-k/2)=k(k+3)=0
k=-3or0(reject)[k≠0]

1b)
Put k=-3
f(x)=8x^3+(4(-3)+4)x^2-4x-3
f(x)=8x^3+(-8)x^2-4x-3
f(x)=8x^3-8x^2-4x-3
f(x)可被2x+k
so f(x)可被 2x-3整除
By長除
f(x)=(2x-3)(4x^2+2x+1)