Use synthetic division to determine which of the following are the real zeroes of the function f(x) = 3x^3 + 10x^2 + 4x - 8

option b is correct

Step-by-step explanation:

In the options a, c and d we have to check if 2 is a root.

The coefficients of  f(x) = 3x^3 + 10x^2 + 4x - 8 are: 3, 10, 4 and -8.

The division of f(x) by (x-2) using synthetic division is:

2          3             10             4              -8

                           6             32              72

           3             16            36              64

The remainder is 64, so 2 is not root of f(x); if it was the remainder would be zero. This result makes options a, c and d incorrect.

The division of f(x) by (x+2) using synthetic division is:

-2          3             10             4              -8

                           -6             -8              8

            3               4            -4               0

The remainder is 0, so -2 is root of f(x).

The division of f(x) by (x-2/3) using synthetic division is:

2/3        3             10             4              -8

                           2               8               8

            3               12           12             0

The remainder is 0, so 2/3 is root of f(x). Then, option b is correct

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>