How do you find a polynomial function that has zeros 0, -2, -3?
Since we are given the zeroes of the polynomial function, we can write the solution in terms of factors.
In general, given 3 zeroes of a polynomial function, a, b, and c, we can write the function as the multiplication of the factors
In this case, we can show that each of a, b, and c are zeroes of the function:
Since the value of the function at x=a, b and c is equal to 0, then the function
With the generalized form, we can substitute for the given zeroes,
From here, we can put it in standard polynomial form by foiling the right side:
And distributing the x yields a final answer of:
To double check the answer, just plug in the given zeroes, and ensure the value of the function at those points is equal to 0.
Thus, the function has zeroes as given by x=0, -2, and -3.