Question

factorise : x cube + 13x square + 32x + 20

Answer 1

${x}^{3} + 13x + 32x + 20 \\ \\ = > {x}^{3} + {x}^{2} + {12x}^{2} + 32x + 20 \\ \\ = > {x}^{2} (x + 1) + 12 {x}^{2} + (12 +20)x + 20 \\ \\ = > {x}^{2} (x + 1) + 12 {x}^{2} + 12x + 20x + 20 \\ \\ = > {x}^{2} (x + 1) + 12x(x + 1) + 20(x + 1) \\ \\ = > (x + 1)( {x}^{2} + 12x + 20) \\ \\ = > (x + 1)( {x}^{2} + 10x + 2x + 20)$


=> ( x + 1 ) [ x( x + 10 ) + 2( x + 10 ) ]


$\bold{ => ( x + 1 )( x + 10 )( x + 2 )}$

Answer 2

Hello dear,

${x}^{3} + 13 {x}^{2} + 32x + 20 \\ \\ = > (x + 1)( {x}^{2} + 12x + 20) \\ \\ [as \: \: for \: \: x = ( - 1) \: \: so \\ \: \: {x}^{3} + 13 {x}^{2} + 32x + 20 =( - 1) + 13 - 32 + 20 = 0 ] \\ \\ = > (x + 1)( {x}^{2} + 10x + 2x + 20) \\ \\ = > (x + 1)[(x(x + 10) + 2(x + 10)] \\ \\ = > (x + 1)(x + 10)(x + 2)$

Hope it helps.