Final answer:
To solve the polynomial 4x³+12x²-9x-27=0, factor out common factors, find additional factors, and solve the resulting quadratic equation.
Step-by-step explanation:
To solve the polynomial 4x³+12x²-9x-27=0, you can use the technique of factoring. First, check if there are any common factors among the terms. In this case, there is a common factor of 3, so you can factor it out: 3(4x³+12x²-9x-27=0). Then, look for any other factors by trial and error or synthetic division. You will find that (x+3) is a factor. Divide the polynomial by (x+3) to get the remaining quadratic expression: 4x²-3. Now, solve the quadratic equation 4x²-3=0 using factoring, completing the square, or the quadratic formula. The solutions to the original polynomial are the roots of the quadratic equation.