Question

factorise x³+13x²+32x+20​

Answer 1

Answer:

Factors are ( x + 1 ) .( x + 2 ) . ( x + 10 )

Step-by-step explanation:

x^3 + 13x^2 + 32x + 20

= ( x + 1 ) . ( x^2 + 12x + 20 )   [∵ for x= -1, x^3 + 13x^2 + 32x + 20

                                                                  = -1 + 13 - 32 + 20 = 33 - 33 = 0 ]

= ( x + 1 ) ( x^2 + 10x + 2x + 20 )

= ( x + 1 ) { x ( x + 10 ) + 2 ( x + 10 ) }

= ( x + 1 ) { ( x + 10 ) .( x + 2 ) }

= ( x + 1 ) .( x + 2 ) . ( x + 10 )

          Factors for the given expression are ( x + 1 ) .( x + 2 ) . ( x + 10 )                    

Answer 2

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

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