Final answer:
To factorize the polynomial p(x), we start with the known factor (x - 3/2) because p(3/2) = 0. Then, we divide the polynomial by this factor to obtain a quadratic equation, which we can solve using the quadratic formula to find the remaining factors.
Step-by-step explanation:
The question involves finding the factorization of a cubic polynomial p(x) given that p(3/2) = 0. Since p(3/2) = 0, we can conclude that x - 3/2 is a factor of the polynomial p(x). To factorize p(x), we can divide the polynomial by x - 3/2 using either synthetic division or long division to find other factors.
After finding one factor, we'll have a quadratic equation which we can solve by applying the quadratic formula ¨ax² + bx + c = 0¨. The solutions to this quadratic will give us the remaining factors of the cubic polynomial, provided that they are real numbers. If complex roots are present, we would state them as such in the factorization.
Remember: whenever a polynomial is given as having a specific value (such as zero) for a particular input, the corresponding (x - value) is a factor of that polynomial.