Using your answers to the previous problem:

1. Factor $f\left(x\right) = x^{3} − 5x^{2} + 11x − 15$.

2. Solve $f\left(x\right) = 0.$

   Step 1 (a):

   Use a generic rectangle to see if x − 3 is a factor.

   Step 2 (a):

   Step 3 (a):

   Step 4 (a):

   Step 5 (a):

   $x^{2} − 2x + 5$

   Answer (a):

   $\left(x − 3\right)\left(x^{2} − 2x + 5\right)$

   

   

   

   

   Step 1 (b):

   Use the factors to solve for $x$.

   $\left(x − 3\right)\left(x^{2} − 2x + 5\right)$

   Answer 1 (b):

   $x = 3$

   Step 2 (b):

   Use the quadratic formula to solve the other factor.

   $x=\frac{2\pm\sqrt{4-20}}{2}$

   Answer 2 (b):

   $x = 1 ± 2i$

   Answer 3 (b):

   $x = {3, 1 ± 2i}$