Big-Exponent Polynomial

Algebra Level 4

Peter picked 4 positive integers a,b,ca, b, c and dd. He wanted to determine the polynomial f(x)= f(x)= (1 ⁣ ⁣x)a+b+c+d(1 ⁣+ ⁣x)a+b+c(1 ⁣ ⁣x ⁣+ ⁣x2)a+b(1 ⁣+ ⁣x ⁣+ ⁣x2)a \small (1\!-\!x)^{a+b+c+d} (1\!+\!x)^{a+b+c}(1\!-\!x\!+\!x^2)^{a+b}(1\!+\!x\!+\!x^2)^a . He felt lazy and ignored any term that involved xx taken to a power larger than or equal to 3. He was surprised to see that the result was the term 121x 1-21x . What is the value of cc?

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