Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x^5+x^4-x^3+x^2-x+2\)
\(=x^5-x^4+x^3-x^2+x+2x^4-2x^3+2x^2-2x+2\)
\(=x\left(x^4-x^3+x^2-x+1\right)+2\left(x^4-x^3+x^2-x+1\right)\)
\(=\left(x+2\right)\left(x^4-x^3+x^2-x+1\right)\)
\(=x^2+x-3x-3.=x\times\left(x+1\right)-3\times\left(x+1\right)=\left(x+1\right).\left(x-3\right)\)
\(x^2-2x-3\)
\(=x^2-3x+x-3\)
\(=x\left(x-3\right)+\left(x-3\right)\)
\(=\left(x-3\right)\left(x+1\right)\)
\(x^2\left(x^2+4\right)-x^2+4\)
\(=x^4+4x^2-x^2+4\)
\(=x^4+3x^2+4\)
\(=x^4-x^3+x^3+2x^2+2x^2-x^2-2x+2x+4\)
\(=\left(x^4-x^3+2x^2\right)+\left(x^3-x^2+2x\right)+\left(2x^2-2x+4\right)\)
\(=x^2\left(x^2-x+2\right)+x\left(x^2-x+2\right)+2\left(x^2-x+2\right)\)
\(=\left(x^2+x+2\right)\left(x^2-x+2\right)\)
Ta có : x7 + x2 + 1
= x7 - x + x + x2 + 1
= (x7 - x) + (x2 + x + 1)
= x(x6 - 1) + (x2 + x + 1)
= x(x3 - 1)(x3 + 1) + (x2 + x + 1)
= x(x - 1)(x2 + x + 1).(x3 + 1) + (x2 + x + 1)
= (x2 + x + 1)[x(x - 1).(x3 + 1) + 1]
= (x2 + x + 1) (x5 - x4 + x2 - x + 1)
Ta co:
\(x^2+x-2011.2012=x^2+x-\left(2012-1\right).2012\)
\(=x^2+x-2012^2+2012=\left(x^2-2012^2\right)+\left(x+2012\right)\) \(=\left(x+2012\right)\left(x-2012\right)+\left(x+2012\right)=\left(x+2012\right)\left(x-2012+1\right)\)
\(=\left(x+2012\right)\left(x-2011\right)\)
thanks nhiều ạ