Question

Hopelessly loss in New Joisey If Anyone can help me I greatly appericate it. Anyone know how do we find the greatest common factor of a polynomial? Can you give me an example,
showing your work.

2.When finding the greatest common factor of a polynomial, can it ever be larger than the smallest
coefficient?

3. Can it ever be smaller than the smallest coefficient?

4. Can anyone Provide me an example.

Answer 1

12x^3y^2 + 48x^6y^4 - 60xy^2

first look at the constant coefficients:
12, 48, 60, their hightest common factor is 12
now look at the x's
x^3 , x^6 , x , their highest common factor is x
and for the y's
y^2 , y^4, and y^2, the highest common factor is y^2
so
= 12xy^2(x^2 + 4x^5y^2 - 5)


always mentally expand your answer to make sure you get back the original.

Had my last term be -50xy^2
then the HCF of the coefficients would have to be only 2

With that you should be able to answer the remaining questions.