Question

which term can be used in the blank of $36x^{3}-22x^{2}-$__ so the greatest common factor of the resulting polynomial is $2x$?
choose two correct answers.
24
$4xy$
$12x$
2
$44y$

Explanation:

Step1: Analyze GCF requirement

We need a term where $\gcd(36x^3, 22x^2, \text{blank term}) = 2x$. This means the term must be divisible by $2x$, and have no larger common factor with the first two terms.

Step2: Check each option

• For 24: $\gcd(36x^3,22x^2,24)=2$, not $2x$. Reject.
• For $4xy$: $\gcd(36x^3,22x^2,4xy)=2x$. Accept.
• For $12x$: $\gcd(36x^3,22x^2,12x)=2x$. Accept.
• For 2: $\gcd(36x^3,22x^2,2)=2$, not $2x$. Reject.
• For $44y$: $\gcd(36x^3,22x^2,44y)=2$, not $2x$. Reject.

Answer:

B. $4xy$, C. $12x$