Question

In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

$Zeros:-3,0,4,degree3$

Short answer

The polynomial function is$f\left(x\right)=x^3-x^2-12x$

Step-by-step solution

Step 1. Given Information

The zeros of the polynomial are$-3,0,4$and degree is 3

Step 2. Forming polynomial Function

If$r$is a real zero of a polynomial function$f,$then$x-r$is a factor of$f.$This means that$x-\left(-3\right)=\left(x+3\right)and\left(x-0\right),\left(x-4\right)$are factors of$f.$As a result, any polynomial function is of the form$f\left(x\right)=a\left(x+3\right)x\left(x-4\right)$

Step 3. Solving the polynomial function

$$\begin{gathered} f\left(x\right)=a\left(x+3\right)x\left(x-4\right) \\ f\left(x\right)=x\left(x+3\right)\left(x-4\right) \\ f\left(x\right)=x\left(x^2-x-12\right) \\ f\left(x\right)=x^3-x^2-12x \end{gathered}$$