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.