Polynomial intersection question

[transgalactic]

V1={cx^3+ax^2|c,a exists in R}
V2={dx^3-bx^2 -d|d,b exists in R}
find all the values of a,b that $$f(x)\epsilon V1\cap V2$$
??

find all the values of a,b that $$f(x)\epsilon V1+ V2$$
??
i know how to solve such question using vectors
but
they are not using using vector but some hoe check the coefficients

??l

 

[Mark44]

Can you list a specific function (with numbers instead of c and a) that belongs to V1? Can you list a specific function (with numbers instead of d and b) that belongs to V2?

What does it take for a function to belong to both V1 and V2; i.e., to $V1 \cap V2$?

 

[transgalactic]

V1 and V2 are subspaces of $$R_4[x]$$
polynomial field over R of power smaller then 4

f(x)=ax^3 +bx^2 +ax -b which belongs to $$R_4[x]$$

that all i am given
no numbes

 

[Mark44]

I know what you're given. Can you use the information that you are given, and give me a specific function (with numbers instead of c and a) that belongs to V1? Can you list a specific function (with numbers instead of d and b) that belongs to V2?

What does it take for a function to belong to both V1 and V2; i.e., to $V1 \cap V2$
?

 

[HallsofIvy]

V1={cx^3+ax^2|c,a exists in R}
V2={dx^3-bx^2 -d|d,b exists in R}
find all the values of a,b that $$f(x)\epsilon V1\cap V2$$
??

find all the values of a,b that $$f(x)\epsilon V1+ V2$$
??

Was that exactly what the problem says? It looks to me like you will need a specific choice for d and c rather than a, b. For example if c= d= 0, then your functions reduce to ax^2 and -bx^2.

i know how to solve such question using vectors
but
they are not using using vector but some hoe check the coefficients

??l