Final answer:
To find the polynomial with zeros -\u221A3, \u221A3, and 4, you multiply the corresponding factors together, yielding the polynomial expression x^3 - 4x^2 - 3x + 12.
Step-by-step explanation:
The polynomial expression that has the zeros -\u221A3, \u221A3, and 4 can be formed by using the fact that if x=a is a zero of the polynomial, then (x-a) is a factor of the polynomial. Therefore, each zero gives us a factor of the polynomial: For -\u221A3: the factor is (x + \u221A3), For \u221A3: the factor is (x - \u221A3), For 4: the factor is (x - 4). To find the polynomial, we multiply these factors together: (x + \u221A3)(x - \u221A3)(x - 4). First, notice that the first two factors are a difference of squares; thus, we multiply them to get: (x2 - 3)(x - 4). Next, we expand this expression by distributing (x - 4) across the binomial: x3 - 4x2 - 3x + 12. So, the polynomial expression with zeros -\u221A3, \u221A3, and 4 is x3 - 4x2 - 3x + 12.