Question

Phân tích đa thức sau thành nhân tử:

a) x³ + 6x² + 11x + 6

b) x³ + 6x² - 13x - 42

c) (x² + x + 4)² + 8x (x² + x +4) + 15x²

d) (x + 2) (x + 4) (x + 6) (x + 8) + 16

Answer 1

a) \(x^3+x^2+5x^2+5x+6x+6=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2+5x+6\right)=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)

b) \(x^3-3x^2+9x^2-27x+14x-42\)

\(=x^2\left(x+3\right)+9x\left(x+3\right)+14\left(x+3\right)\)

\(=\left(x^2+9x+14\right)\left(x+3\right)\)

\(=\left(x+3\right)\left(x+2\right)\left(x+7\right)\)

c) \(\left(x^2+x+4\right)^2+3x\left(x^2+x+4\right)+5x\left(x^2+x+4\right)+15x^2\)

\(=\left(x^2+x+4\right)\left(x^2+x+4+3x\right)+5x\left(x^2+x+4+3x\right)\)

\(=\left(x^2+6x+4\right)\left(x^2+4x+4\right)\)

\(=\left(x^2+6x+4\right)\left(x+2\right)^2\)

d) \(\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+16\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)

\(=\left(x^2+10x\right)^2+40\left(x^2+10x\right)+16.24+16\)

\(=\left(x^2+10x\right)^2+40\left(x^2+10x\right)+400\)

\(=\left(x^2+10x+20\right)^2\)