Question

Phân tích thành nhân tử:

1. x(x + 2)(x + 3)(x + 5) + 9

2. 8x⁴ + 30x² + 7

3. (x² - x + 1)(x² + 3x + 1) + 4x²

4. x³ + x² - 2x + 8

Answer 1

\(x\left(x+2\right)\left(x+3\right)\left(x+5\right)+9=\left[x\left(x+5\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]+9=\left(x^2+5x\right)\left(x^2+5x+6\right)+9.Dat:x^2+5x=a\Rightarrow x\left(x+2\right)\left(x+3\right)\left(x+5\right)+9=a\left(a+6\right)+9=a^2+6a+9=\left(a+3\right)^2=\left(x^2+5x+3\right)^2\)

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