câu ở dưới mình ghi sai đề

x⁴+2002x²+2001x+2002

mk đang cần gấp lắm.mọi người giúp mk nha.ai nhanh tay nhất mk k cho

\(x^4+2002x^2+2001x+2002\)

\(=x^4+x^2+1+2001x^2+2001x+2001\)

\(=\left(x^4+2x^2+1\right)-x^2+2001\left(x^2+x+1\right)\)

\(=\left(x^2+1-x\right)\left(x^2+1+x\right)+2001\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2+1-x+2001\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2002\right)\)

\(x^4+2007x^2-2006x+2007\)

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

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

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

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

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

a) \(x^5+x+1=\left(x^5+x+1\right)=x\left(x^4+1+\frac{1}{x}\right)\)

b) và c) Tương tự nha

Chả biết đúng hay sai :v tại dùng máy tính tính ra kết quả rồi phân tích ngược lại

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

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

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

b)\(x^4+2002x^2+2001x+2002=x^4+x^3+1-x^3+x^2+x+2002x^2+2002x+1\)

 \(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2002\left(x^2+x+1\right)\)

\(=\left(x^2-x+2002\right)\left(x^2+x+1\right)\)

c)Tương tự câu a),ta phân tích được:

  \(x^{11}+x^7+1=\left(x^2+x+1\right)\left(x^9-x^8+x^6-x^4+x^3-x+1\right)\)

Ta có: \(x^4+2002x^2+2001x+2002\)

\(=x^4+x^3-x^3+x^2-x^2+2002x^2+2002x-x+2002\)

\(=x^4+x^3+x^2-x^3-x^2-x+2002x^2+2002x+2002\)

\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2002\left(x^2+x+1\right)\)

\(=\left(x^2-x+2002\right)\left(x^2+x+1\right)\)

\(=\left(x^4+x^3+2002x^2\right)-\left(x^3-x^2+2002x\right)+x^2+x+2002\)

\(=x^2\left(x^2+x+2002\right)-x\left(x^2+x+2002\right)+x^2+x+2002\)

\(=\left(x^2-x+1\right)\left(x^2+x+2002\right)\)

\(x^4-x^2+2x+2\)

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

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

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

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

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

\(x^4-x^2+2x+2\)

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

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

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

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

\(\dfrac{1}{4}x^2+2xy+4y^2=\left(\dfrac{1}{2}x+2y\right)^2\)