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QUESTION Show that any real cubic polynomial can be expressed in
the form $$\alpha x^{(3)}+\beta x^{(2)}+\gamma x^{(1)}+\delta
x^{(0)}$$ where $x^{(3)}=x(x-1)(x-2)$.

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ANSWER $$ax^3+bx^2+cx+d=ax^{(3)}+(3a+b)x^{(2)}+(a+b+c)x^{(1)}+d$$


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