Question

Which term can be used in the blank of 36x3−22x2−__ so the greatest common factor of the resulting polynomial is 2x? Select two options.

2
4xy
12x
24
44y

Answer 1

Given:

The expression is:

`36x^3-22x^2-\_\_\_`

To find:

The values for the blank so that the greatest common factor of the resulting polynomial is
`2x`.

Solution:

We have,

`36x^3-22x^2-\_\_\_`

If the greatest common factor of the resulting polynomial is
`2x`, then 2 and x must be factors of missing value.

In option A, 2 is a factor of 2 but
`x` is not a factor of 2. So, this option is incorrect.

In option B, 2 and
`x` are factors of
`4xy`. So, this option is correct.

In option C, 2 and
`x` are factors of
`12x`. So, this option is correct.

In option D, 2 is a factor of 24 but
`x` is not a factor of 24. So, this option is incorrect.

In option E, 2 is a factor of
`44y` but
`x` is not a factor of
`44y`. So, this option is incorrect.

It means the correct value for the given blank is either
`4xy` or
`12x`.

Therefore, the correct options are B and C.