Question

Phân tích thành nhân tử

(\(\left(x^2+6x+5\right)\left(x^2+10x+21\right)+15\)

Answer 1

\(\left(x^2+6x+15\right)\left(x^2+10x+21\right)+15=\left(x+5\right)\left(x+1\right)\left(x+3\right)\left(x+7\right)+15=\left(x+5\right)\left(x+3\right)\left(x+1\right)\left(x+7\right)+15=\left(x^2+8x+15\right)\left(x^2+8x+7\right)+15\)

Đặt \(x^2+8x+7=a\)

Khi đó pt thành \(a\left(a+8\right)+15=a^2+8a+15=\left(a+3\right)\left(a+5\right)\)

Do đó: \(\left(x^2+6x+5\right)\left(x^2+10x+21\right)+15=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)