Division Algorithm For Polynomials

[keelejody]

Im given two polynomials:

f(x) =(2x^6) + (x^5) - (3x^4) + (4x^3) + (x^2) -1
and
g(x)=(x^3)-(x^2)+2x+3

find polynomials Q(x),R(x) in the set of R[x] s.t

f(x) =g(x)Q(X) +R(X) and deg(R)<deg(g)

Am i even in the right area? and something to do with manipulating numbers in C[x]

does g divide f or g is a factor of f if there exists polynomial h s.t f=gh

im so confused. sorry i can't communicate my thoughts well, but I am very much stuck

 

[Mark44]

Im given two polynomials:

f(x) =(2x^6) + (x^5) - (3x^4) + (4x^3) + (x^2) -1
and
g(x)=(x^3)-(x^2)+2x+3

find polynomials Q(x),R(x) in the set of R[x] s.t

f(x) =g(x)Q(X) +R(X) and deg(R)<deg(g)

What is the "set of R[x]"?

It looks like what you're asked to do is to write f(x) as the product of two polynomials plus a remainder. Do you know how to do polynomial long division? When you do the division you will get Q(x) = 2x^3 + lower degree terms. If g(x) is a factor of f(x), R(x) will be 0. Otherwise, R(x) will be a polynomial of degree two or lower.

Am i even in the right area? and something to do with manipulating numbers in C[x]

does g divide f or g is a factor of f if there exists polynomial h s.t f=gh

im so confused. sorry i can't communicate my thoughts well, but I am very much stuck

 

[keelejody]

its remainder and quotient...obvious now. thanks