Question

Isiah determined that 5a2 is the GCF of the polynomial
a3 – 25a2b5 – 35b4. Is he correct? Explain.

Answer 1

Answer:

No, Isiah is not correct. The GCF of the coefficients is 1, and there are no common variables among all three terms of the polynomial. 5b4 is a factor of -25a2b5 and -35b4, but not a3. Additionally, a2 is a factor of a3 and -25a2b5, but not -35b4. 1 is the GCF of the coefficients. There are no common variables among all three terms of the polynomial.  5b4 is the GCF of –25a2b5 and –35b4, but not a3.  a2 is a factor of a3 and – 25a2b5, but not –35b4.

Answer 2

Considering the multiplciation of the GCF of the numeric terms and of the variables, the GCF of the polynomial is of 1, hence he is not correct.

What is the greatest common factor of a polynomial?

It is the multiplication of the GCF of the numeric constants by the GCF of the coefficients.

In this problem:

• The coefficients of a are 3, 2 and 0, hence the GCF is $a^0$.

• The coefficients of b are 0, 5 and 4, hence the GCF is $b^0$.

• As for the numeric term, the terms are 1, 25 and 35, hence the GCF is 1.

Thus:

$a^0 \times b^0 \times 1 = 1$

As Isaiah did not take into account the coefficients that are zero, his calculation is not correct.

More can be learned about the greatest common factor at https://brainly.com/question/6032811