To identify the mystery term in the polynomial 20x²y + 56x³, given that 4x² is the greatest common factor (GCF), we first need to confirm the GCF and see how it relates to the polynomial’s terms.
The GCF of 20x²y and 56x³ can be determined by looking for the highest factors common to both terms:
- For the numerical coefficients: 20 and 56
- 20 = 2^2 × 5
- 56 = 2^3 × 7
- Here, the GCF of the coefficients is determined by taking the lowest power of the common prime factor:
- 2 is common, and its lowest power is 2^2 (4).
- For the variable part:
- In 20x²y, we have x² and y.
- In 56x³, we have x³.
- The GCF for the variables is the lowest power of common variables, which is x² since both terms contain it.
Putting it all together, the GCF of 20x²y + 56x³ is indeed 4x².
Next, we can factor out the GCF to find the resulting expression:
20x²y + 56x³ = 4x²(5y + 14x)
This means that the remaining term, or the mystery term, after factoring out 4x² from the original polynomial is:
5y + 14x.
Thus, if 4x² is the GCF of the polynomial 20x²y + 56x³, the mystery term could be 5y + 14x.