The cool name is Cool Symmetry. Part II

Algebra Level 4

If \(A_0(x),A_1(x), \text{ and } A_2(x)\) are the three polynomials

and \(a_0,a_1,\text{ and } a_2\) are three distinct real numbers, then \[(a_1+a_2)A_0(x)+(a_2+a_0)A_1(x)+(a_0+a_1)A_2(x)= ?\]

\[A_0(x)=\dfrac{(x-a_1)(x-a_2)}{(a_0-a_1)(a_0-a_2)} \] \[ A_1(x)=\dfrac{(x-a_0)(x-a_2)}{(a_1-a_0)(a_1-a_2)}\] \[ A_2(x)=\dfrac{(x-a_0)(x-a_1)}{(a_2-a_0)(a_2-a_1)} \] \[ A(x)=(x-a_0)(x-a_1)(x-a_2)\]

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