To determine the mystery term, we first need to understand what the GCF (Greatest Common Factor) is. In our case, we know that the GCF of the polynomial terms is 4x².
Now, let’s break down the given polynomial terms:
- 20x²y: We can factor this term by breaking it down:
- 20 = 4 × 5
- x² = x²
- y = y
- 56x³: We can also factor this term:
- 56 = 4 × 14
- x³ = x³
Since the GCF is 4x², we can factor that out of both terms:
- From 20x²y, if we factor out 4x², we get:
- 20x²y ÷ 4x² = 5y
- From 56x³, if we factor out 4x², we get:
- 56x³ ÷ 4x² = 14x
Now we have:
- 20x²y = 4x²(5y)
- 56x³ = 4x²(14x)
To identify the mystery term, we can express the polynomial in its factored form:
4x²(5y + 14x)
Therefore, the mystery term formed along with the GCF could be (5y + 14x).