Question

Which term can be used in the blank of 36x^3−22x^2−__ so the greatest common factor of the resulting polynomial is 2x? Select two options.

1) 2
2) 4xy
3) 12x
4) 24
5) 44y

Answer 1

2) 4xy

3) 12x

Explanation:

You can figure this out by seeing which answer can have a 2x factored out of it.

4xy = 2x(2y)

12x = 2x(6)

The other answers dont have an x in it so you cant factor out a 2x from them.

Answer 2

Option 2 and 3

Explanation:

Given : Expression
`36x^3-22x^2-\_`

To find : Which term can be used in the blank of expression so the greatest common factor of the resulting polynomial is 2x ?

Solution :

From the following options first we have to determine that it contain 2x.

1) 2- x is missing

2) 4xy - 2x is present

So,
`36x^3-22x^2-4xy=2x(18x^2-11x-2y)`

3) 12x - 2x is present

So,
`36x^3-22x^2-12x=2x(18x^2-11x-6)`

4) 24 - x is missing

5) 44y - x is missing

Therefore, The required terms are 4xy and 12x.

So option 2 and 3 is correct.