Chapter 0, Problem 13PR

a)

To determine

To write: the expression for the two numbers.

Answer to Problem 13PR

The numbers are $\left(x+5\right)$ and $\left(x-1\right)$ .

Explanation of Solution

Given information:

It is given that there are two integers. One is 5 more than a number, and the other is 1 less than the same number.

Let the number be ‘x’.

Then, one number is $\left(x+5\right)$ .

Another number is $\left(x-1\right)$ .

So, the numbers are $\left(x+5\right)$ and $\left(x-1\right)$ .

b)

To determine

To write: the polynomial expression for the product of the numbers.

Answer to Problem 13PR

The polynomial expression for the product is $x^2+4x-5$ .

Explanation of Solution

Given information:

It is given that there are two integers. One is 5 more than a number, and the other is 1 less than the same number.

Let the number be ‘x’.

Then, one number is $\left(x+5\right)$ .

Another number is $\left(x-1\right)$ .

So, the numbers are $\left(x+5\right)$ and $\left(x-1\right)$ .

Now, finding the product,

  $\begin{array}{c}\left(x+5\right)\left(x-1\right)=x\left(x-1\right)+5\left(x-1\right)\\ =x^2-x+5x-5\\ =x^2+4x-5\end{array}$

So, the polynomial expression for the product is $x^2+4x-5$ .