Question

Factor the given polynomial by finding the greatest common monomial factor (or the negative of the greatest common monomial factor) and rewrite the expression.

49x^3y+21xy^2

Answer 1

To factor out the greatest common monomial factor from the given polynomial 49x^3y + 21xy^2, we need to find the largest monomial that can divide both terms evenly.

The monomial with the smallest exponent for x is x, and the monomial with the smallest exponent for y is y. So the smallest possible monomial that can divide both terms evenly is xy.

Now, let's divide each term by the common factor:

49x^3y / xy = 49x^2
21xy^2 / xy = 21y

So, the factored form of the polynomial is:

xy(49x^2 + 21y)