Question

Phân tích đa thức thành nhân tử: x(x+4)(x+6)(x+10)+128

Answer 1

Kết quả : (x + 8)(x + 2)(x² + 10x + 8)

Answer 2

\(x\left(x+4\right)\left(x+6\right)\left(x+10\right)+128\)

\(=x\left(x+10\right)\left(x+4\right)\left(x+6\right)+128\)

\(=\left(x^2+10x\right)\left(x^2+10x+24\right)+128\)

\(=\left(x^2+10x\right)^2+24\left(x^2+10x\right)+128\)

\(=\left(x^2+10x\right)^2+2.\left(x^2+10x\right).12+12^2-16\)

\(=\left(x^2+10x+12\right)^2-4^2\)

\(=\left(x^2+10x+12-4\right) \left(x^2+10x +12+4\right)\)

\(=\left(x^2+10x-8\right)\left(x^2+10x+16\right)\)

\(=\left(x^2+10x-8\right)\left(x^2+2x+8x+16\right)\)

\(=\left(x^2+10x-8\right)\left[x\left(x+2\right)+8\left(x+2\right)\right]\)

\(=\left(x^2+10x-8\right)\left(x+2\right)\left(x+8\right)\)