Question

Phân tích đa thức thành nhân tử : 
5x³ + 38x² + 19x - 14

Answer 1

5x³ + 38x² + 19x - 14

= ( 5x³ + 35x² ) + ( 3x² + 21x ) - ( 2x + 14 )

= 5x² ( x + 7 ) + 3x ( x + 7 ) - 2 ( x + 7 )

= ( x + 7 ) ( 5x² + 3x - 2 ) 

= ( x + 7 ) [ ( 5x² - 2x ) + ( 5x - 2 ) ]

= ( x + 7 ) [ x ( 5x - 2 ) + ( 5x - 2 ) ]

= ( x + 7 ) ( x + 1 ) ( 5x - 2 )    

Answer 2

\(5x^3+38x^2+19x-4\)

\(=\left(5x^3+35x^2\right)+\left(3x^2+21x\right)-\left(2x+14\right)\)

\(=5x^2\left(x+7\right)+3x\left(x+7\right)-2\left(x+7\right)\)

\(=\left(5x^2+3x-2\right)\left(x+7\right)\)

\(=\left(5x^2-2x+5x-2\right)\left(x+7\right)\)

\(=\left[x\left(5x-2\right)+\left(5x-2\right)\right]\left(x+7\right)\)

\(=\left(x+1\right)\left(5x-2\right)\left(x+7\right)\)