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f(x)=p(x)(x−1)+1f(x)=q(x)(x−2)+1f(x)=r(x)(x−3)+1 \begin{aligned} f(x) &=& p(x)(x-1) +1 \\ f(x) &=& q(x)(x-2) +1 \\ f(x) &=& r(x)(x-3) +1 \end{aligned} f(x)f(x)f(x)===p(x)(x−1)+1q(x)(x−2)+1r(x)(x−3)+1
Let f(x)f(x)f(x) be a cubic monic polynomial, and p(x),q(x),r(x)p(x), q(x), r(x)p(x),q(x),r(x) be quadratic polynomials satisfying the system of equations above.
What is the value of f(4)?f(4)?f(4)?
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