Final answer:
To solve the equation 3x³+15x²+12x=0 given that one of the linear factors is x+4, we can factor out x from the equation, divide both sides by x, and then solve the resulting quadratic equation.
Step-by-step explanation:
To solve the equation 3x³+15x²+12x=0 given that one of the linear factors is x+4, we can start by factoring out x from the equation:
x(3x²+15x+12)=0
Next, we can divide both sides of the equation by x, which gives us:
3x²+15x+12=0
Now we can solve the quadratic equation by factoring or using the quadratic formula. Factoring the quadratic equation gives us:
(x+3)(3x+4)=0
Setting each factor equal to zero, we have:
x+3=0 or 3x+4=0
Solving these equations, we find that x=-3 or x=-4/3. Therefore, the solutions to the equation are x=-4, -3, and -4/3.