Question

Factor x3-2x2-9x+18 completely if(x+3) is a factor

Answer 1

Factor x^3 -2x^2-9x+18

= x^2(x - 2) - 9(x - 2)

= (x^2 - 9)(x -2)

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

So (x+3) is a factor

Answer 2

Dividing:-

x + 3) x^3 - 2x^2 - 9x + 18 {  x^2 - 5x + 6

        x^3 + 3x^2

       ----------------

              -5x^2 - 9x

              -5x^2 - 15x

              ----------------

                           6x  + 18

                            6x + 18

                            .............

The quotient is x^2 - 5x + 6

which is  (x - 3)(x - 2)

So the factors of the original expression

= (x + 3)(x - 3)(x - 2)   answer