(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to find a basis for the following:

S = {f are polynomials of degree less than or equal to 4| f(0) = f(1) = 0}

2. The attempt at a solution

A general polymial is of the form:

p(x) = ax^4 + bx^3 + cx^2 + dx + e

Now for p(0) = p(1) = 0 I must have:

e = 0 and a + b + c + d + e = 0

Which basically becomes:

a + b + c + d = 0.

Here is where I get stuck. I'd usually solve for a variable and then substitute it back into the polynomial and then group like coefficients to get a basis, but it just isn't working!

Any help?

NEVERMIND!!!!!!!!!!!!!!! I've figured out what I was doing wrong lol Apparently I don't know how to factor LOL

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# Basis of a subspace

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