# Basis of 4th degree polynomial linear space that doesn't contain 2nd or 3rd degree polynomials

In K4[x], the linear space of the polynomials of degree 4 or less with coefficients in in K, determine:

(a) A basis that doesn't contain 2nd or 3rd degree polynomials

(b) If there exists a basis that doesn't contain 4th degree polynomials

(c) A supplementary subspace of the one generated by the polynomials p(x)=−1+2x+x^2 y q(x)=1+x+x^2

Suggestion: use coordinate row (or column) matrices

• Hi Chachi Kent! Welcome to MSE. It is very helpful to potential answerers if you format your post using MathJax. That way it's easy to read and thus easier to answer – eepperly16 Dec 12 '17 at 20:00
• What are your thoughts? Do you understand what the "suggestion" is saying? – angryavian Dec 12 '17 at 20:23
• That the coefficients of the polynomial(s) would form the rows/columns of a matrix, right? But if there's no 2nd or 3rd degree, two whole rows of the martix would be null or would just two elements of it be null? – Chachi Kent Dec 13 '17 at 9:45