Chapter 3, Problem 39RE

(a)

To determine

To calculate : the zeroes of the polynomial

Answer to Problem 39RE

The zeroes are $0,4,-4$

Explanation of Solution

Given information : The polynomial is $P\left(x\right)=x^3-16x$

Calculation :

The zeros of the polynomial is obtained as:

  $\begin{array}{l}P\left(x\right)=x^3-16x\\ \Rightarrow P\left(x\right)=x\left(x^2-16\right)=0\\ \Rightarrow P\left(x\right)=x\left(x^2-4^2\right)=0\\ \Rightarrow P\left(x\right)=x\left(x-4\right)\left(x+4\right)=0\\ x=0\Rightarrow \boxed{x=0}\\ x-4=0\Rightarrow \boxed{x=4}\\ x+4=0\Rightarrow \boxed{x=-4}\end{array}$

Hence,

The zeroes are $0,4,-4$

(b)

To determine

To sketch : the graph of polynomial $P\left(x\right)=x^3-16x$

Explanation of Solution

Given information : The polynomial is $P\left(x\right)=x^3-16x$

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{P\left(x\right)}$ button.

Step 3: Enter the expression $x^3-16x$ which is required to graph.

Step 4: Press $\boxed{\text{GRAPH}}$ button to graph the function.

The graph is obtained as:

  

Interpretation : The above graph is of polynomial $P\left(x\right)=x^3-16x$