isiah determined that $5a^{2}$ is the gcf of the polynomial $a^{3}-25a^{2}b^{5}-35b^{4}$. is he correct…

Answer:

No, he is not correct.

Explanation:

Step1: Analyze each term's factors

The factors of $a^{3}=a\times a\times a$. The factors of $25a^{2}b^{5}=5\times5\times a\times a\times b\times b\times b\times b\times b$. The factors of $35b^{4}=5\times7\times b\times b\times b\times b$.

Step2: Identify the GCF

The common factors among all three terms are only $1$. The term $a^{3}$ has no $b$ - terms and the last two terms have no $a$ - terms with non - zero exponents in common with $a^{3}$ in a way that would allow for a non - trivial common factor involving both $a$ and $b$. Also, the first term has no factor of $5$ other than $1$. So the GCF of $a^{3}-25a^{2}b^{5}-35b^{4}$ is $1$, not $5a^{2}$.