Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=-18.
If a polynomial of degree 3 has zeros at -3, -1, and 4, the polynomial will have this form:
f(x) = a·(x + 3)·(x + 1)·(x - 4)
Since f(-2) = 18, we can find the value for a by solving:
18 = a·(-2 + 3)·(-2 + 1)·(-2 - 4)
Find the value of a and substitute this into:
f(x) = a·(x + 3)·(x + 1)·(x - 4)