Question

Phân tích đa thức thành nhân tử:

a ) \(x^2+5x+6\)

b ) \(x^2\left(1-x^2\right)-4+4x^2\)

Answer 1

a ) \(x^2+5x+6\)

\(=x^2+5x+\frac{25}{4}-\frac{1}{4}\)

\(=\left(x+\frac{5}{2}\right)^2-\frac{1}{4}\)

b ) \(x^2\left(1-x^2\right)-4+4x^2\)

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

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

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

Answer 2

a) \(x^2+5x+6\\ =x^2+5x+\frac{25}{4}-\frac{1}{4}\\ =\left(x+\frac{5}{2}\right)^2-\frac{1}{4}\\ \)

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