Question

Rút gọn:

\(A=x^6-2007.x^5+2007.x^4-2007.x^3+2007.x^2-2007.x+2007\) ( với x=2006)

Answer 1

\(A=x^6-2007x^5+2007x^4-2007x^3+2007x^2-2007x+2007\)

\(=x^6-2006x^5-x^5+2006x^4+x^4-2006x^3-x^3+2006x^2+x^2-2006x-x+2006+1\)

\(=x^5\left(x-2006\right)-x^4\left(x-2006\right)+x^3\left(x-2006\right)-x^2\left(x-2006\right)+x\left(x-2006\right)-\left(x-2006\right)+1\)

\(=\left(x^5-x^4+x^3-x^2+x-1\right)\left(x-2006\right)+1\)

Thay x = 2006

\(\Leftrightarrow A=1\)

Vậy A = 1 tại x = 2006

Answer 2

\(A=x^6-2007.x^5+2007.x^4-2007.x^3+2007.x^2-2007.x+2007\)

\(=x^6-\left(x+1\right).x^5+\left(x+1\right).x^4-...+x+1\)

\(=x^6-x^6-x^5+x^5+x^4-x^4-...-x+1\)

\(=1\)