a)\(x^8+2x^4+1-x^4=\left(x^4+1\right)^2-\left(x^2\right)^2\)

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

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

\(=\left(x^4+x^3+x^2\right)-\left(x^3-2007x^2-2007x-2008\right)\)

\(=x^2\left(x^2+x+1\right)-\left[x\left(x^2+x+1\right)-2008\left(x^2-x-1\right)\right]\)

\(=x^2\left(x^2+x+1\right)-\left(x^2+x+1\right)\left(x-2008\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

Câu \(\left(x^2+x+1\right)\left(x^2-x+2008\right)\) là câu b nha!Quên ghi đề

mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

  x^4 + 2008x^2 + 2007x + 2008

\(=x^4+x^2+2007x^2+2007x+2007+1\)

\(=x^4+x^2+1+2007\left(x^2+x+1\right)\)

\(=\left(x^2+1\right)^2-x^2+2007\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1\right)+2007\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

       x⁴+2008x²+2007x+2008

<=> x⁴-x+2008x²+2008x+2008

<=> x(x³-1)+2008(x²+x+1)

<=> x(x-1)(x²+x+1)+2008(x²+x+1)

<=> (x²+x+1)(x²-x+2008)

x^4+2008x^2+2007x+2008

=x^4+2008x^2+2008x-x+2008

=(x^4-x)+(2008x^2+2008x+2008)

=x(x^3-1)+2008(x^2+x+1)

=x(x-1)(x^2+x+1)+2008(x^2+x+1)

=(x^2+x+1)(x^2-x+2008)

\(\left(x^4+x^2+1\right)+\left(2007x^2+2007x+2007\right)\)

=\(\left(x^2+x+1\right)\left(x^2-x+1\right)+2007\left(x^2+x+1\right)\)

=\(\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

x^4_x+2008(x²+x+1)=x(x-1)(x2+x+1)+2008(x2+x+1)=(x2-x+2008)(x2+x+1)

a) \(x^8+x+1\)

\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)

b) \(x^4+2008x^2+2007x+2008\)

\(=x^4+x^3+x^2-x^3-x^2-x+2008x^2+2008x+2008\)

\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2008\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

\(x^8+x+1\)

\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+x^2+x+1\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)

2x^4 hay x^4

=x⁴+2008x²+2008x-x+2008

=(x⁴-x)+(2008x²+2008x+2008)

=x(x³-1)+2008(x²+x+1)

=x(x-1)(x²+x+1)+2008(x²+x+1)

=(x²+x++1)(x²-x+2008)

http://olm.vn/hoi-dap/question/684622.html

Bạn có thể học hỏi ở đó

tíck mik nha