數學＊10分

其實因式定理同餘式定理係差唔多..
唔同o既..只係計出o黎答案係零就係因式..
唔係零就係餘式..
不過之前o既答案你覺得唔o岩..就睇o下我幫唔幫到你啦~

設f(x)=2kx^3 + 7x^2 - 5x -3k
f(x)=(2x+3)Q(x)+6 [Q(x)係商..]
so....
2kx^3 + 7x^2 - 5x -3k=(2x+3)Q(x)-6
代x=(-3/2)
2k(-3/2)^3 + 7(-3/2)^2 - 5(-3/2) -3k=[2(-3/2)+3]Q(-3/2)-6
-27k/4+63/4+15/2-3k=-6
-27k+63+30-12k=-24
-39k=-117
k=3

設f(x)=2kx^3 + 7x^2 - 5x -3k
f(-3/2)=-6
f(-3/2)=2k(-3/2)^3+7(-3/2)^2-5(-3/2)-3K
-6=-6.75k+23.25-3k
-29.25= -9.75k
k=3