Chapter 3, Problem 1RCC

a.

To determine

To write the defining equation for a polynomial P of degree n.

Answer to Problem 1RCC

The defining equation for a polynomial P of degree n is :

$\text{P}\left(\text{x}\right){\text{=a}}_{\text{n}}{\text{x}}^{\text{n}}{\text{+a}}_{\text{n}-\text{1}}{\text{x}}^{\text{n}-\text{1}}\text{+}\mathrm{...}{\text{+a}}_{\text{1}}{\text{x+a}}_{\text{0}}$

Explanation of Solution

Given information:

A polynomial P of degree n.

The defining equation for a polynomial P of degree n is :

$\text{P}\left(\text{x}\right){\text{=a}}_{\text{n}}{\text{x}}^{\text{n}}{\text{+a}}_{\text{n}-\text{1}}{\text{x}}^{\text{n}-\text{1}}\text{+}\mathrm{...}{\text{+a}}_{\text{1}}{\text{x+a}}_{\text{0}}$

Where n is a non-negative integer and ${\text{a}}_{\text{n}}\ne 0$ .

b.

To determine

To determine the meaning of “c is a zero of P”

Answer to Problem 1RCC

Hence, c is a zero of P means the value of the function $\text{P}\left(\text{c}\right)=0$

Explanation of Solution

Given information:

The given statement is

“What does it mean to say that c is a zero of P”

If P is a polynomial function and c is a real number.

Then, c is a zero of P means the value of the function $\text{P}\left(\text{c}\right)=0$