relational database - Is this BCNF correct? -

i given problem find out bcnf of relation converted 3nf. asks ,

1) find key ,

2) convert bcnf.

relation

student(studentid,courseid,lecturerid,grade) 

fds

{studentid,courseid} -> grade {studentid,courseid} -> lecturerid  lecturerid -> courseid 

what got far

1) since ${studentid,courseid}$ can have attributes in closure of {studentid,courseid}, key composite attribute. that's got first question.

2) has asked provide bcnf of given relation. considering first fd can see satisfies bcnf since left side consist of key attribute.

im using decomposition algorithm here

so considering second fd, consists of key composite attribute in left side. satisfies bcnf.

in third 1 see doesn't satisfy bcnf. have split relation.

r1 : (lecturerid,courseid)  r2 : (lecturerid, studentid, grade) 

so r1 , r2 relations answers.

my problem

i need check answers 1 , 2. can please verify that. thank you.