Questions: Solve the equation by factoring. (Enter your answers as a comma-separated list.) a^3+3 a^2-16 a-48=0 a=

Solution Steps

To solve the cubic equation by factoring, we first look for possible rational roots using the Rational Root Theorem. Once a root is found, we can use polynomial division to factor the cubic polynomial into a product of a linear factor and a quadratic factor. Finally, we solve the quadratic equation to find the remaining roots.

We start with the cubic equation given by:

\[ a^{3} + 3a^{2} - 16a - 48 = 0 \]

By factoring the cubic polynomial, we find the roots of the equation. The roots are:

\[ a = -4, \quad a = -3, \quad a = 4 \]

Final Answer