Questions: Solve the following polynomial equations by grouping and factoring, x^3 - 4x^2 - 4x + 16 = 0. Select one: A. x=4,2,-2 B. x=2,4,-4 C. x=0,-4,2 D. x=4,2

Solution Steps

We start with the polynomial equation:

\[ x^{3} - 4x^{2} - 4x + 16 = 0 \]

By grouping and factoring, we can express this polynomial as:

\[ (x - 4)(x - 2)(x + 2) = 0 \]

To find the roots of the polynomial, we set each factor equal to zero:

1. \(x - 4 = 0 \implies x = 4\)
2. \(x - 2 = 0 \implies x = 2\)
3. \(x + 2 = 0 \implies x = -2\)

Thus, the solutions to the polynomial equation are:

\[ x = 4, \quad x = 2, \quad x = -2 \]

Final Answer