Ta có: \(x^2-19x-30=\frac{4x^2-76x-120}{4}\)
\(=\frac{1}{4}.\left[\left(4x^2-76x+361\right)-481\right]\)
\(=\frac{1}{4}.\left[\left(2x-19\right)^2-481\right]\)
\(=\frac{1}{4}.\left(2x-19-\sqrt{481}\right).\left(2x-19+\sqrt{481}\right)\)
Nghiệm xấu nên phân tích khó :) Sửa thành x3 - 19x - 30 cho dễ
x3 - 19x - 30
= x3 + 3x2 - 3x2 - 9x - 10x - 30
= ( x3 + 3x2 ) - ( 3x2 + 9x ) - ( 10x + 30 )
= x2( x + 3 ) - 3x( x + 3 ) - 10( x + 3 )
= ( x + 3 )( x2 - 3x - 10 )
= ( x + 3 )( x2 + 2x - 5x - 10 )
= ( x + 3 )[ x( x + 2 ) - 5( x + 2 ) ]
= ( x + 3 )( x + 2 )( x - 5 )
\(x^2-19x-30=\left(x-\frac{19+\sqrt{481}}{2}\right)\left(x-\frac{19-\sqrt{481}}{2}\right)\)
