Solution
First, find the GCF of the expression. The GCF of
6,45, and
21 is
3. The GCF of
x3,x2, and
x is
x. (Note that the GCF of a set of expressions in the form
xn will always be the exponent of lowest degree.) And the GCF of
y3,y2, and
y is
y. Combine these to find the GCF of the polynomial,
3xy.
Next, determine what the GCF needs to be multiplied by to obtain each term of the polynomial. We find that
3xy(2x2y2)=6x3y3,3xy(15xy)=45x2y2, and
3xy(7)=21xy.
Finally, write the factored expression as the product of the GCF and the sum of the terms we needed to multiply by.
(3xy)(2x2y2+15xy+7)