Chapter 0.2, Problem 17E

a)

To determine

the expressions for the two numbers.

Answer to Problem 17E

Expressions for two numbers is $\left(x-7\right)$ and $\left(x+2\right)$ .

Explanation of Solution

Given information :

It is given that there are two integers. One is 7 less than a number, and the other is 2 greater than the same number.

Let the number be x.

According to the question,

First number = $\left(x-7\right)$

Second number = $\left(x+2\right)$

So,

Expressions for two numbers is $\left(x-7\right)$ and $\left(x+2\right)$ .

b)

To determine

the polynomial expression for the product of the numbers.

Answer to Problem 17E

The expression after product of the numbers is $x^2-5x-14$ .

Explanation of Solution

Given information :

It is given that there are two integers. One is 7 less than a number, and the other is 2 greater than the same number.

According to the question,

First number = $\left(x-7\right)$

Second number = $\left(x+2\right)$

So,

Polynomial expression for product of the numbers is $\left(x-7\right)\left(x+2\right)$ .

After simplifying it,

  $\begin{array}{c}\left(x-7\right)\left(x+2\right)=x^2-7x+2x-14\\ =x^2-5x-14\end{array}$

So, the expression after product of the numbers is $x^2-5x-14$ .