x=4

=>x+1=5

A=(x+1)x^5 -(x+1)x^4+(x+1)x^3-(x+1)x^2+(x+1)x-1

  =x^6+x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2-x+1

  =x^6-x-1

  =4^6-4-1

  =4091

\(a,A=5\cdot4^5-5\cdot4^4+5\cdot4^3-5\cdot4^2+5\cdot4+1\\ A=4^4\left(20-5\right)+4^2\left(20-5\right)+\left(20-5\right)\\ A=15\left(4^4+4^2+1\right)=15\cdot273=4095\)

\(b,x=7\Leftrightarrow x+1=8\\ \Leftrightarrow B=x^{2006}-\left(x+1\right)x^{2005}+\left(x+1\right)x^{2004}-...+\left(x+1\right)x^2-\left(x+1\right)x-5\\ B=x^{2006}-x^{2006}-x^{2005}+x^{2005}+x^{2004}-...+x^3+x^2-x^2-x-5\\ B=-x-5=-12\)

b)tương tự

=x^2006-x^2006-x^2005+x^2005+x^2004-...+x^3-x^2-x^2-x-5

=-x-5

=-7-5=-12

a) 

\(P=\left(x^{14}-9x^{13}\right)-\left(x^{13}-9x^{12}\right)+\left(x^{12}-9x^{11}\right)-...+\left(x^2-9x\right)-\left(x-9\right)+1\)

\(=x^{13}\left(x-9\right)-x^{12}\left(x-9\right)+x^{11}\left(x-9\right)+...+x\left(x-9\right)-\left(x-9\right)+1\)

\(P\left(9\right)=1\)

b)

\(Q=\left(x^{15}-7x^{14}\right)-\left(x^{14}-7x^{13}\right)+\left(x^{13}-7x^{12}\right)-...-\left(x^2-7x\right)+\left(x-7\right)+2\)

\(=x^{14}\left(x-7\right)-x^{13}\left(x-7\right)+x^{12}\left(x-7\right)-...-x\left(x-7\right)+\left(x-7\right)+2\)

\(Q\left(7\right)=2\)

ghi lại đề tý

\(B=x^{15}-8x^{14}+8x^{13}-8x^2+...-8x^2+8x-5\)

=> \(B=x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-\left(x+1\right)x^{12}+...+\left(x+1\right)x-x+2\)

=>\(B=x^{15}-x^{15}+x^{14}-x^{14}+x^{13}-x^{13}-x^{12}+...+x^2+x-x+2\\\)

=>B=2

x=7 nên x+1=8

\(B=x^{15}-x^{14}\left(x+1\right)+x^{13}\left(x+1\right)-x^{12}\left(x+1\right)+...-x^2\left(x+1\right)+x\left(x+1\right)-5\)

\(=x^{15}-x^{15}-x^{14}+x^{14}-x^{13}+x^{13}-...-x^3-x^2+x^2+x+5\)

=x+5

=7+5

=12

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

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

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

\(=-2\)

\(3x^2-15x^2+8x^2\)

\(=-4x^2\)

Thay \(x=\dfrac{1}{4}\) vào biểu thức ta được: 

\(-4\cdot\left(\dfrac{1}{4}\right)^2=-\dfrac{1}{4}\)

Vậy: ...

ta có: 8=7+1=x+1

\(B=x^{15}-8x^{14}+8x^{13}-...-8x^2+8x-5\)

\(\Rightarrow B=x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-...-\left(x+1\right)x^2+\left(x+1\right)x-5\)

\(\Rightarrow B=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-...-x^3-x^2+x^2+x-5\)

\(\Rightarrow B=x-5\)

\(\Rightarrow B=7-5\)

\(\Rightarrow B=2\)

B = x15 - 8x14 + 8x13 - 8x2 + ... - 8x2 + 8x - 5

B = x^15 - 7x^14 -x^14+7x^13+x^13-7x^12-...-x^2+7x+x-5

B = x^14(x-7) - x^14(x-7) +...+x^2(x-7)-x(x-7)+x-5

B = 7-5=2

B = x15 - 8x14 + 8x13 - 8x2 + ... - 8x2 + 8x - 5

B = x^15 - 7x^14 -x^14+7x^13+x^13-7x^12-...-x^2+7x+x-5

B = x^14(x-7) - x^14(x-7) +...+x^2(x-7)-x(x-7)+x-5

B = 7-5=2

Tham khảo cách này nhoá~