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Suppose that P is the polynomial of least degree with integer coefficients such that P ( 7 + 5 )=2( 7 - 5 ) . Find P (2) .

Correct answer

40

Step-by-step solution

Let 7 + 5 = x then aligned & P(x)=( 7 + 5 )( 7 - 5 )( 7 - 5 ) since 2=( 7 + 5 )( 7 - 5 ) & =( 7 + 5 )( 7 - 5 )^2 & =( 7 + 5 ) (24-( 7 + 5 )^2 ) & P(x)=x (24-x^2 ) & P(2)=2(24-4) & aligned

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