Question

phân tích đa thức thành nhân tử bằng phương pháp thêm- bớt hạng tử :

x^4 +4

A^4 + 64

x^5 + x + 1

x^5 + x - 1

Answer 1

x^4+4=x^4 + 4x^2 +4 - 4x^2=(x^2)^2+ 2.x^2.2+2^2 - (2x)^2 = (x^2+2)-(2x)^2 =(x^2+2-2x)(2^2+2-2x)

Answer 2

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

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

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

Answer 3

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

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

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

Answer 4

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

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

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