Question

Phân tích đa thức thành nhân tử:

a) x⁴ -5x² +4

Answer 1

x⁴ - 5x² + 4

= x⁴ - x² - 4x² + 4

= x²( x² - 1) - 4( x² - 1)

= ( x² - 1)( x² - 2²)

= ( x - 1)( x + 1)( x - 2)( x + 2)

Answer 2

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

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

Answer 3

Answer 4

x⁴ - 5x² + 4

= x⁴ - x² - 4x² + 4

= x²( x² - 1) - 4( x² - 1)

= ( x² - 1)( x² - 2²)

= ( x - 1)( x + 1)( x - 4)( x + 4)

Answer 5

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

Answer 6

x⁴ - 5x² + 4

= x⁴ - x² - 4x² + 4

= x²( x² - 1) - 4( x² - 1)

= ( x² - 1)( x² - 2²)

= ( x - 1)( x + 1)( x - 2)( x + 2)