Question

what is the factored form of y=x^3+3x^2-x-3 and what the zeros

Answer 1

   y = x³ + 3x² - x - 3
   0 = x³ + 3x² - x - 3
   0 = x²(x) + x²(3) - 1(x) - 1(3)
   0 = x²(x + 3) - 1(x + 3)
   0 = (x² - 1)(x + 3)
   0 = (x² + x - x - 1)(x + 3)
   0 = (x(x) + x(1) - 1(x) - 1(1))(x + 3)
   0 = (x(x + 1) - 1(x + 1))(x + 3)
   0 = (x - 1)(x + 1)(x + 3)
   0 = x - 1    or    0 = x + 1    or    0 = x + 3
+ 1      + 1         - 1        - 1         - 3        - 3
   1 = x      or      -1 = x       or      -3 = x

Solution Set: {-3, -1, 1}