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.

$x^2+4x-5$