Construct a polynomial function with the following properties: third degree , only real coefficients, -3 and 2 + I are two of the zeros, y-intercepts is -30. Please explain how to get the answer and what the answer is.
Since all coefficients of the polynomial are real and one of the zeros is 2 + i, the polynomial must also have a conjugate zero 2 - i. The degree of the polynomial is 3, so it must have three zeros and can be written as
P(x) = A(x - x_1)(x - x_2)(x - x_3) where A is a constant.
Write P(x) = A(x - (-3))(x - 2 - i)(x - 2 + i) =
A(x + 3)(x - 2 - i)(x - 2 + i) = use the formula (a - b)(a + b) = a^2 - b^2 where a = x - 2, b = i