Question

factorise 2x^3+19x^2+38x+21

Answer 1

To factorise -

2x³ + 19x² + 38x + 21

Solution -

2x³ + 19x² + 38x + 21

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

=> 2x³ + 14x² + 5x² + 35x + 3x + 21

=> 2x³ + 5x² + 15x + 14x² + 35x + 21

=> [ 2x³ + 5x² + 15x ] + [ 14x² + 35x + 21 ]

=> x [ 2x² + 5x + 3 ] + 7 [ 2x² + 5x + 3 ]

=> ( x + 7 )( 2x² + 5x + 3 )

=> ( x + 7 )( 2x² + 2x + 3x + 3 )

=> ( x + 7 )( 2x{ x + 1 } + 3 { x + 1 } )

=> ( x + 7 )( x + 1)( x + 3)

This is the required answer .

_______________________________

Answer 2

Step-by-step explanation:

$\huge \underline{ \mathfrak{ \red{Given}}} : -$

• $\sf \: factorise \: 2x^3+19x^2+38x+21$

$\huge \underline{ \mathfrak{ \red{to \: find}}} : -$

• $\mathfrak{ \orange{simplyfy \: the \: \: given \: \: factory}}$

$\huge \underline{ \mathfrak{ \red{solution}}} : -$

$\sf \to \: 2x^3 + 19x^2+ 38x + 21 \\ \\ \sf \to \: {x}^{2} ( {x}^{2} + x) + 38x + 21 \\ \\ \sf \to \: x\:( x+ x) {x}^{2} + 38x + 21 \\ \\ \sf \to \: \:(x + x)x(x + 38) + 21 \\ \\ \sf \to \red{(x + x) ( x + 21)(x + 38) }$