## Pruning a subset

Hi, I sort of understand how to prune just number vectors, but these polynomial type questions i am finding a bit tricky, here is one of the questions.

Let $P_{3}(R)$ denote the vector space of real polynomial functions of degree less than or equal to three. Consider the subset $X = \{f1, f2, f3, f4\} \subset P_{3}(R)$ with
$f_{1}(x) = 3x^3 + 2x^2 - x +7$,
$f_{2}(x) = 7x^3 + 5x^2 + 4x + 3$,
$f_{3}(x) = x^3 + x^2 + 6x - 11$,
and $f_{4}(x) = 11x^3 + 8x^2 + x + 2$.

Prune $X$ to produce a linearly independent subset $Y$ such that $Span(Y) = Span(X)$.