a) x2 + 3x - 18 = 0
⇔ x2 - 3x + 6x - 18 = 0
⇔ x( x - 3 ) + 6( x - 3 ) = 0
⇔ ( x - 3 )( x + 6 ) = 0
⇔ x - 3 = 0 hoặc x + 6 = 0
⇔ x = 3 hoặc x = -6
b) x3 - x2 - 4 = 0
⇔ x3 - 2x2 + x2 - 4 = 0
⇔ x2( x - 2 ) + ( x - 2 )( x + 2 ) = 0
⇔ ( x - 2 )( x2 + x + 2 ) = 0
⇔ x - 2 = 0 hoặc x2 + x + 2 = 0
⇔ x = 2 < do x2 + x + 2 = ( x2 + x + 1/4 ) + 7/4 = ( x + 1/2 )2 + 7/4 ≥ 7/4 > 0 ∀ x
b) x3 - 6x2 - x + 30 = 0
⇔ x3 - 5x2 - x2 + 5x - 6x + 30 = 0
⇔ x2( x - 5 ) - x( x - 5 ) - 6( x - 5 ) = 0
⇔ ( x - 5 )( x2 - x - 6 ) = 0
⇔ ( x - 5 )( x2 - 3x + 2x - 6 ) = 0
⇔ ( x - 5 )[ x( x - 3 ) + 2( x - 3 ) ] = 0
⇔ ( x - 5 )( x - 3 )( x + 2 ) = 0
⇔ x - 5 = 0 hoặc x - 3 = 0 hoặc x + 2 = 0
⇔ x = 5 hoặc x = 3 hoặc x = -2
