Question

Chứng minh rằng 

                           f(x) = ( x^2 - 3x + 1 ) ^2015 - ( x^2 - 4x + 5 ) ^2016 + 2 chia hết cho ( x - 2 ) 

  

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Answer 1

\(f\left(x\right)=\left(x^2-3x+1\right)^{2015}-\left(x^2-4x+5\right)^{2016}+2\)

\(f\left(x\right)=\left(x^2-4x+4+x+3\right)^{2015}-\left(x^2-4x+4+1\right)^{2016}+2\)

\(f\left(x\right)=B\left(x-2\right)+\left(x+3\right)^{2015}-B\left(x-2\right)-1+2\)

\(f\left(x\right)=B_1\left(x-2\right)-B_2\left(x-2\right)+\left(x-2+5\right)^{2015}+1\)

\(f\left(x\right)=B_1\left(x-2\right)-B_2\left(x-2\right)+B_3\left(x-2\right)+5^{2015}+1\)

Chỉ chia hết cho x-2 khi 5^2015+1 chia hết cho x-2