Question

The polynomial p is a function of x. The graph of p has four zeros at -4, -23, 0, and 9. Select all the expressions that could represent p.

3x(x−4)(x+23)(x+9)

-x(x+4)(x+23)(x−9)

-3x(x+4)(3x+2)(x−9)

3x(x+4)(2x−3)(x−9)

-3x(x+4)(3x+2)(x−9)2

Answer 1

The expression that can represent the polynomial p is that:

-3x(x + 4)(3x + 2)(x − 9)

What is the Polynomial Expression?

We are told that there are four zeros of the polynomial which are:

-4, -2/3, 0 and 9

Now, if the zero of a polynomial is a, then it means that (x - a) is a factor.

Thus, the factors of the polynomial are:

(x + 4)

(3x + 2)

x

(x - 9)

Thus, the expression that can represent the polynomial p is that:

-3x(x + 4)(3x + 2)(x − 9)