Question

Solve the polynomial equation:x^3 64. do not round. leave answers and exact form.

a) x = 2
b) x = -2
c) x = 4
d) x = -4

Answer 1

The solutions to the polynomial equation x^3 - 64 are x = 4 and two complex solutions.

Step-by-step explanation:

The polynomial equation x^3 - 64 can be factored using the difference of cubes formula:

(x - 4)(x^2 + 4x + 16) = 0

To solve for x, we set each factor equal to zero:

1. (x - 4) = 0, so x = 4
2. (x^2 + 4x + 16) = 0 is a quadratic equation and can be solved using the quadratic formula. However, the solutions are complex and cannot be expressed in exact form.

Therefore, the solutions to the polynomial equation x^3 - 64 are x = 4 and two complex solutions.