Question

Phân tích đa thức thành nhân tử

a, (x² + x)² + 3(x² + x) + 2

b, x ( x + 1) ( x + 2 ) ( x+ 3) + 1

c,( x² + x + 1) (x² + 3x + 1) + x²

d, ( x + 1) (x + 2) (x + 30) (x + 4) - 24

Answer 1

a: \(=\left(x^2+x+1\right)\left(x^2+x+2\right)\)

b: \(=\left(x^2+3x\right)\left(x^2+3x+2\right)+1\)

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

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

c: \(=\left(x^2+1\right)^2+4x\left(x^2+1\right)+4x^2\)

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

d: \(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)\)

\(=x\left(x+5\right)\left(x^2+5x+10\right)\)