Question

$4x^2$ is the gcf of this polynomial. $20x^2y + 56x^3 -?$ which could be the mystery term? $22x^3$ $24x^2y$ $28x^2y$ $28y^3$

Explanation:

Step1: Recall GCF requirements

The GCF $4x^2$ must divide every term of the polynomial. This means each term must be a multiple of $4$ and contain $x^2$ as a factor.

Step2: Check Option 1 ($22x^3$)

Factor of $22$: $\gcd(22,4)=2
eq4$. Reject this option.

Step3: Check Option 2 ($24x^2y$)

Factor of $24$: $\gcd(24,4)=4$, and term has $x^2$. This fits.

Step4: Verify remaining options

Option3 ($26x^2y$): $\gcd(26,4)=2
eq4$. Reject.
Option4 ($28y^3$): No $x^2$ factor. Reject.

Answer:

24$x^2y$