Question

please solve this sum

Answer 1

Solution 1.)

x^3 - 2x^2 - x + 2

= x^2 ( x - 2) - 1 ( x - 2)

= (x - 2) (x^2 - 1)

= ( x - 2) [ (x)^2 - (1)^2]

= (x-2) (x +1) (x - 1)

Solution 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 + 10x + 2x + 20]

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

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

Answer 2

(1) x³ - 2x² - x + 2

x² ( x - 2 ) - 1 ( x - 2 )

( x - 2 ) ( x² - 1 )

( x - 2 ) { ( x)² - (1)² }

( x - 1 ) ( x + 1 ) ( x - 1 ).

(2) x³+ 13x² + 32x + 20

x³ + x² + 12x² + 12x + 20x + 20

x² ( x + 1 ) + 12x ( x + 1 ) + 20 ( x + 1 )

( x + 1 ) ( x² + 12x + 20 )

( x + 1 ) { ( x² + 10x + 2x + 20 ) }

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

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

( x + 1 ) ( x + 10 ) ( x + 2)