Question

Write a polynomial that represents the product of the integer before x and the next consecutive odd integer after x

Answer 1

x(x - 1)

x(x + 1)

(x - 1)(x + 1)

(x + 1)(x + 1)

Answer 2

x is an integer.
The integer before x is 1 less than x.
How would you represent 1 less than x in terms of x?

Answer 3

x(x - 1)

Answer 4

I'm not asking for an answer form the choices. We are only looking for one of the numbers now.

What is 1 less than x?

Answer 5

0

Answer 6

No.
Let me try with numbers.
A number is 8.
What is 1 less than 8?

Answer 7

7

Answer 8

Correct.
What operation did you do to 8 to get the correct answer of 7?

Answer 9

subtraction

Answer 10

Correct.
1 less than 8 means 8 - 1 = 7
1 less than 20 means 20 - 1 = 19
1 less than 100 means 100 - 1 = 99

You follow all those examples?

Answer 11

yep

Answer 12

Now thinking the same way, that 1 less than a number means subtract one form the number, what is 1 less than x?
It is x - 1
We can't simplify x - 1 any more because x and 1 are not like terms.
x - 1 is simply x - 1 and it means whatever number you allow x to be, subtract 1 from it.

Answer 13

Now let's look at the problem again.

Answer 14

ok

Answer 15

Write a polynomial that represents the product of the integer before x and the next consecutive odd integer after x

Answer 16

The integer before x is 1 less than x.
That means the integer before x is x - 1.
We already know that.

Answer 17

yes

Answer 18

The next consecutive integer after x is 1 more than x.
Just like 1 less than x is x - 1, 1 more than x is x + 1.
To show the product of one less than x and one more than x, you do
(x - 1)(x + 1)

Answer 19

so its(x - 1)(x + 1)?

Answer 20

Yes.