Write the cubic polynomial function f(x) in expanded form with zeros −5,−2, and −1, given that f(−3)=4.

Using the Factor Theorem, the polynomial function is given by:

The Factor Theorem states that a polynomial function with roots is given by:

In which a is the leading coefficient.

In this problem, we have zeros -5, -2 and -1, thus , and:

f(-3) = 4 means that when , and this is used to find a.

Thus, the function is:

A similar problem is given at link

If a, b and c are zeros of a polynomial function, we can present this function as:

Therefore we have:

We know f(-3) = 4. Substitute x = -3 to the equation of the function f:

Therefore we have:

Use distributive property:

goog may have it for you