Question

one of the factor of polynomial x^3+4x^2-3x-18 is x+3 then factorise the given polynomial

Answer 1

x^3 +4x^2 - 3x - 18

= x^3 + ( 3x^2 + x^2) + ( 3x - 6x) - 18

= x^3 + 3x^2 + x^2 +3x - 6x - 18

= x^2 ( x + 3) + x (x +3) - 6(x +3)

= (x +3)[ x^2 + x - 6]

= (x +3)[ x^2 + 3x - 2x - 6]

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

= (x +3)( x +3)(x - 2)

Answer 2

x^3 +4x^2 - 3x - 18

= x^3 + ( 3x^2 + x^2) + ( 3x - 6x) - 18

= x^3 + 3x^2 + x^2 +3x - 6x - 18

= x^2 ( x + 3) + x (x +3) - 6(x +3)

= (x +3)[ x^2 + x - 6]

= (x +3)[ x^2 + 3x - 2x - 6]

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

= (x +3)( x +3)(x - 2)