What is the multiplicity of each of the roots of the graph of f(x) = 2x4 + 12x} + 16x2 – 12x – 18?
A.-3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1
B.-3, multiplicity 2; 1, multiplicity 2
C.-3, multiplicity 1; -1, multiplicity 1; 1, multiplicity 1
D.-3, multiplicity 2; -1, multiplicity 3; 1, multiplicity 1

The correct option is;

C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1

Please find attached the required function graph

Step-by-step explanation:

To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;

x       F(x)

-4       30

-3       0

-2       6

-1        0

0      -18

1         0

2       150

The shape of a graph with multiplicity of 2

Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;

x = 1, -1, and, giving

(x - 1)·(x + 1)·(x - 3)² = 0

Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.