Question

A polynomial P(x) of degree 4 has zeros of -1, 2, i, and -i, and has a y-intercept of 4. Write a formula for P(x) in standard form. What are the leading term and the leading coefficient?

Answer 1

Were we given a polynomial of degree 4 and asked to find the zeros, one approach would be to factor that polynomial if possible. Then, setting each factor = to zero will produce a root or zero of the polynomial.

Here, we're doing the opposite. If, for example, you know that one of the roots / zeroes of a n unknown polynomial is -1, then a factor of that polynomial is (x-[-1]). Find the other three factors, and then multiply all four factors together.