Step 1:
Write the function.
[tex]f(x)=x^3-x^2\text{ - x - 15}[/tex]
Step 2:
From f(3) = 0
One of the zeros is x = 3
Then one of the factor is x - 3.
Step 3:
Divide the function by x - 3
Step 3:
[tex]\begin{gathered} F\text{ind the zeros of } \\ x^2\text{ + 2x + 5} \\ x\text{ = }\frac{-b\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \text{a = 1, b = 2 and c = 5} \\ \text{x = }\frac{-2\pm\sqrt[]{2^2-4\times1\times5}}{2\times1} \\ x\text{ = }\frac{-2\pm\sqrt[]{4-20}}{2} \\ x\text{ = }\frac{-2\pm\sqrt[]{-16}}{2} \\ \text{x = }\frac{-2\pm i\sqrt[]{16}}{2} \\ \text{x = }\frac{-2\pm4i}{2}\text{ } \\ \text{x = -1 + 2i or -1 - 2i} \end{gathered}[/tex]
Final answer
The zeros are:
3, -1 + 2i , -1 - 2i
