Question

phân tích đa thức thành nhân tử: x³+9x²+26x+24

 

Answer 1

\(x^3+9x^2+26x+24=\left(x^2+7x+12\right)\left(x+2\right)=\left(x+3\right)\left(x+4\right)\left(x+2\right)\)

Answer 2

Ta có: \(x^3+9x^2+26x+24\)

\(=\left(x^3+2x^2\right)+\left(7x^2+14x\right)+\left(12x+24\right)\)

\(=x^2\left(x+2\right)+7x\left(x+2\right)+12\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2+7x+12\right)\)

\(=\left(x+2\right)\left[\left(x^2+3x\right)+\left(4x+12\right)\right]\)

\(=\left(x+2\right)\left[x\left(x+3\right)+4\left(x+3\right)\right]\)

\(=\left(x+2\right)\left(x+3\right)\left(x+4\right)\)

Answer 3

x³ + 9x² + 26x + 24

= x³ + 2x² + 7x + 12x + 14x + 24

= ( x³ + 7x² + 12x ) + ( 2x² + 14x + 24 )

= x( x² + 7x + 12 ) + 2( x² + 7x + 12 )

= ( x² + 7x + 12 )( x + 2 )

= ( x² + 3x + 4x + 12 )( x + 2 )

= [ x( x + 3 ) + 4( x + 3 ) ]( x + 2 )

= ( x + 2 )( x + 3 )( x + 4 )