Question

The polynomial function f(x) has degree 4, a y-intercept of -24, roots of -3

and 4, and a multiplicity 2 root of -1.
a) Enter f(x).

Answer 1

The polynomial function f(x), use the given degree, y-intercept, and roots is f(x) = a(x + 3)(x - 4)(x + 1)^2.

Step-by-step explanation:

The polynomial function f(x) can be determined using the given information:

• degree 4
• y-intercept of -24
• roots of -3 and 4
• multiplicity 2 root of -1

Since the degree of the polynomial is 4, it will have 4 terms.

The y-intercept can be represented by the constant term.

The roots are the values that make the polynomial equal to zero.

The multiplicity of a root represents how many times it appears as a solution.

Therefore, f(x) can be written as: f(x) = a(x + 3)(x - 4)(x + 1)^2, where 'a' represents a constant coefficient of the polynomial.