Final answer:
To find the zeros of the function f(x) = 2x^3 + 4x^2 algebraically, we substitute -4 into the function and solve. The zeros of the function are x = -4, x = 0, and x = -2.
Step-by-step explanation:
To find the zeros of the function f(x) = 2x^3 + 4x^2, we can set f(x) equal to zero and solve for x. In this case, we are given that f(-4) = 0. So we substitute -4 into the function and solve:
2(-4)^3 + 4(-4)^2 = 0
Using the properties of exponents, we simplify this to:
-128 + 64 = 0
Therefore, -4 is one of the zeros of the function. To find the other zeros, we can factor out x.
2x^3 + 4x^2 = x(2x^2 + 4x)
Setting each factor equal to zero, we have:
x = 0
2x^2 + 4x = 0
Factoring out a common factor of 2x:
2x(x + 2) = 0
Setting each factor equal to zero, we have:
x = 0
x + 2 = 0
Therefore, the zeros of the function f(x) = 2x^3 + 4x^2 are x = -4, x = 0, and x = -2.