Question 141
The set of all polynomials of degree less than or equal to $4$ with rational coefficients is considered.
a) Prove that it has vector space structure on the body of rational numbers.
b) Prove that the $1$, $x-2$, $(x-2)^2$, $(x-2)^3$ and $(x-2)^4$ polynomials form a base of this space.
c) Express the polynomial $7+2x-45x^2+3x^4$ on the previous base.
a) Prove that it has vector space structure on the body of rational numbers.
b) Prove that the $1$, $x-2$, $(x-2)^2$, $(x-2)^3$ and $(x-2)^4$ polynomials form a base of this space.
c) Express the polynomial $7+2x-45x^2+3x^4$ on the previous base.