E-PR04 · A three-term factor hides an identity
Let \(P(x)=(1+x+x^2)(1-x)^5\).
Find the first four terms of \((1-x)^5\) in ascending powers of x.
Find the coefficients of \(x^3\) and \(x^4\) in P.
Show that \(P(x)=(1-x^3)(1-x)^4\). Hence state its degree and leading coefficient.
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