Question

Phân tích đa thức thành nhân tử
1, \(2\left(x^2+x\right)^2-\left(9x^2+9x\right)+7\)
2, \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+16\)

Answer 1

1/A= \(2\left(x^2+x\right)^2-9\left(x^2+x\right)+7\)

Đặt \(x^2+x=t\).Ta được:

A=\(2t^2-9t+7=\left(2t-7\right)\left(t-1\right)\)

\(=\left(2x^2+2x-7\right)\left(x^2+x-1\right)\)

2)B= \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+16\)

\(=\left[\left(x+1\right)\left(x+7\right)\right]\left[\left(x+3\right)\left(x+5\right)\right]+16\)

\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+16\)

Đặt \(x^2+8x=t\).Suy ra:

\(B=\left(t+7\right)\left(t+15\right)+16=t^2+22t+121\)

\(=\left(t+11\right)^2=\left(x^2+8x+11\right)^2\)

Đúng không ta?