Question

[Tuyet Thanh Tran]

Phân tích đa thức thành nhân tử

1, \(x^3-9x^2+6x+16\)

2, \(x^3-6x^2-x+30\)

3, \(2x^3-x^2+5x+3\)

4, \(64x^4+y^4\)

5, \(27x^3-27x^2+18x-4\)

Answer 1

[Nguyễn Lê Phước Thịnh]

1: \(=x^3-8x^2-x^2+8x-2x+16\)

\(=\left(x-8\right)\left(x^2-x-2\right)=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)

2: \(=x^3+2x^2-8x^2-16x+15x+30\)

\(=\left(x+2\right)\left(x^2-8x+15\right)\)

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

3: \(=2x^3+x^2-2x^2-x+6x+3\)

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

4: \(=64x^4+16x^2y^2+y^4-16x^2y^2\)

\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)

\(=\left(8x^2-4xy+y^2\right)\left(8x^2+4xy+y^2\right)\)