Question

Phân tích đa thức thành nhân tử :\(x^4+2014x^2+2013x+2014\)

\(x^8+7x^4+16\)

Giúp mk vs, thank trước luôn nha

Answer 1

\(x^4+2014x^2+2013x+2014\)

\(=x^4+2014x^2+2014x-x+2014\)

\(=\left(x^4-x\right)+\left(2014x^2+2014x+2014\right)\)

\(=x\left(x^3-1\right)+2014\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2014\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2014\right)\)

b)\(x^8+7x^4+6\)

\(=x^8+x^4+6x^4+6\)

\(=x^4\left(x^4+1\right)+6\left(x^4+1\right)\)

\(=\left(x^4+1\right)\left(x^4+6\right)\)

Answer 2

b) \(x^8+7x^4+16\)

\(=\left(x^8+8x^4+16\right)-x^4\)

\(=\left[\left(x^4\right)^2+2.x^4.4+4^2\right]-x^4\)

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

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