Question

cho đa thức f(x)=\(x^{17}-2004.x^{16}+2004.x^{15}-2004.x^{14}+...+2004.x-1\) tính giá trị đa thức tại x=2003

Answer 1

f(x)=\(x^{17}-2004.x^{16}+2004.x^{15}-2004.x^{2014}+...+2004.x-1\)

= \(x^{17}-\left(2003+1\right)x^{16}+\left(2003+1\right)x^{15}-\left(2003+1\right)^{14}+...+\left(2003+1\right)-1\)

Thay x = 2003

=> f(x)= \(x^{17}-\left(x+1\right)x^{16}+\left(x+1\right)x^{15}-\left(x+1\right)x^{14}+...+\left(x+1\right)x-1\)

=\(x^{17}-x^{17}-x^{16}+x^{16}+x^{15}-x^{15}-x^{14}+...+x^2+x-1\)

= \(x-1\)

= 2003 -1

=2002