Question

Use synthetic division to determine which of the following are the real zeros of the function

f(x)=3x ^3 +10x ^2+4x−8.

Options:
Option 1: -2
Option 2: 1
Option 3: 2
Option 4: -1

Answer 1

To determine the real zeros of the function f(x)=3x^3+10x^2+4x-8, we can use synthetic division with the given options. The real zeros are 1 and 2.

Step-by-step explanation:

To use synthetic division, we need to find the zeros of the function f(x)=3x^3+10x^2+4x-8. We can start by trying the given options -2, 1, 2, and -1 using synthetic division. If the remainder is zero, then that option is a real zero of the function.

Using synthetic division with option -2, we get a remainder of -10, which is not zero. Using option 1, we get a remainder of 0, so 1 is a real zero. Using option 2, we get a remainder of 0 as well, so 2 is a real zero. Lastly, using option -1, we get a remainder of -14, which is not zero. Therefore, the real zeros of the function are 1 and 2.