please factorize this... y= x^3 - x^2 - 5x - 3

Question

the question ask me to factorise and find the x- and y- intercepts for the graph.

 

please help,

 

thank you

Answer 1

you can establish that this cubic equation has 1 positive root and either 2 negative roots or 2 imaginary roots. So there is no guarantee that 3 is a root and x-3 is a factor. It is a trial and error process. It turned out that 3 is a root because when the polynomial is divided by x-3, there is no remainder. the quotient x2 +2x +1 then provided two remaining factors (x+1) and (x+1) and a duplicate root of -1.
 
Other possible roots were +1 and -3. Of course if you had divided the polynomial by (x-1) or (x+3), there would have been a remainder.

Answer 2

    

        x²+2x+1

     _________

x-3l  x³-x²-5x-3

       x³-3x²

      _______

           2x²-5x

           2x²-6x

          ________

                  x-3

 

x²+2x+1=(x+1)(x+1)

x³-x²-5x-3=(x+1)(x+1)(x-3)

x-intercepts are -1 and 3

Answer 3

>> y inter is -3

Correct, y intersect is determined by x = 0

 

>>...is (x-1)(x-3)(x-1) correct??

(x-3)*(x-1)*(x-1)

=(x-3)*(x^2 - 2x + 1)

=(x^3 - 2x^2 + x) - 3*(x^2 - 2x + 1)

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

=x^3 + x^2 + 7x - 3

No, that's not right

 

(Changed, after Arthur D. pointed out a +/- error in my original posting.)