To determine if Isiah is correct, we need to find the greatest common factor (GCF) of the polynomial terms: a³, 25a²b⁵, and 35b⁴.
First, let’s break down each term:
- a³: This term has a factor of a raised to the 3rd power.
- 25a²b⁵: This term has a coefficient of 25 (which factors into 5 × 5), a², and b raised to the 5th power.
- 35b⁴: This term has a coefficient of 35 (which factors into 5 × 7), and b raised to the 4th power.
Next, we identify the GCF for each component:
- For the coefficients: The GCF of 25 and 35 is 5, as 5 is the greatest number that divides both.
- For the variable a: The lowest power of a present in the terms is a² (this is in the second term).
- For the variable b: The lowest power of b is b⁰ (which is 1, present in the first term), since the first term has no ‘b’.
Putting this together, the GCF is:
5a² (from 5 for the coefficients and a² for the a terms). The ‘b’ is not included because the first term has no b.
Thus, Isiah is correct in stating that 5a² is the GCF of the polynomial a³ + 25a²b⁵ + 35b⁴.