Questions: What are the zeros of (f(x)=2 x^3+18 x^2+40 x ?) Enter your answers, from least to greatest, in the boxes. The zeros are and and

Solution Steps

To find the zeros of the polynomial function \( f(x) = 2x^3 + 18x^2 + 40x \), we need to solve the equation \( f(x) = 0 \). First, factor out the greatest common factor from the polynomial. Then, solve the resulting equation by setting each factor equal to zero and solving for \( x \).

To find the zeros of the polynomial \( f(x) = 2x^3 + 18x^2 + 40x \), we first factor out the greatest common factor, which is \( 2x \). This gives us: \[ f(x) = 2x(x + 4)(x + 5) \]

Set each factor equal to zero and solve for \( x \):

1. \( 2x = 0 \) gives \( x = 0 \).
2. \( x + 4 = 0 \) gives \( x = -4 \).
3. \( x + 5 = 0 \) gives \( x = -5 \).

Arrange the zeros from least to greatest: \( x = -5, -4, 0 \).

Final Answer