Question

There are two integers. One is 5 more than a number, and the other is 1 less than the same number. A. Write expressions for the two numbers. B. Write a polynomial expression for the product of the numbers

Answer 1

Given that there are two integers:

- One is 5 more than a number.

- The other integer is 1 less than the same number.

Let be "x" the same number.

A. You can identify that "5 more than a number" indicates Addition. Therefore, you can write this expression for the first integer:

`x+5`

You can also identify that "1 less than the same number" indicates Subtraction. Then, you can write this expression to represent the second integer:

`x-1`

B. By definition, a Product is the result of a Multiplication.

Therefore, you need to write the Multiplication of the expressions found in Part A:

`(x+5)(x-1)`

In order to write a polynomial expression for the Product of the integer numbers, you can multiply the expressions. You can apply the FOIL Method and, which states that:

`(a+b)(c+d)=ac+ad+bc+bd`

And then adding the like terms. You get:

`=(x)(x)-(x)(1)+(5)(x)-(5)(1)`
`=x^2-x+5x-5`
`=x^2+4x-5`

Hence, the answers are:

A. - Expression for the first integer number:

`x+5`

- Expression for the second integer number:

`x-1`

B.

`x^2+4x-5`