Question

\(X^4+2016x^2+2015x+2016\)Phân tích đa thức thành nha tử

 

Answer 1

Ta có: x^4 + 2016x^2 + 2015x + 2016

= x^4 + x^3 + x^2 - x^3 - x^2 - x + 2016x^2 + 2016x + 2016

= x^2(x^2 + x + 1) - x(x^2 + x + 1) + 2016(x^2 + x + 1)

= (x^2 + x + 1)(x^2 - x + 2016)

Answer 2

       \(x^4+2016x^2+2015x+2016\)

\(=x^4-x+2016x^2+2016x+2016\)

\(=x\left(x^3-1\right)+2016\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2016\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2016\right)\)

Answer 3

\(x^4+2016x^2+2015x+2016\)

\(=x^4+2015x^2+x^2+2015x+2015+1\)

\(=\left(x^4+2x^2+1-x^2\right)+\left(2015x^2+2015x+2015\right)\)

\(=\left(x^4+2x^2+1\right)-x^2+2015\left(x^2+x+1\right)\)

\(=\left(x^2+1\right)^2-x^2+2015\left(x^2+x+1\right)\)

\(=\left(x^2+1+x\right)\left(x^2+1-x\right)+2015\left(x^2+x+1\right)\)

\(=\left(x^2+1+x\right)\left(x^2-x+2016\right)\)