# Find the GCF of each product.

(2x2+5x)(7x - 14)

(6y2 -3y)( y+7)

When the term "Greatest Common Factor" is used, it applies to a pair of numbers. The terms you have liated are polynomials that have already been factored. They could be further factored into

7x(2x+5)(x-2)

and

3y(2y-1)(y+7)

These two terms do not have a common factor, other than 1.

## In the expression (2x^2+5x)(7x - 14), you can factor out a common factor of x:

x(2x+5)(7x - 14)

In the expression (6y^2 - 3y)(y+7), you can factor out a common factor of 3y:

3y(2y - 1)(y+7)

The greatest common factor (GCF) of each product is x for the first expression and 3y for the second expression.

## To find the greatest common factor (GCF) of each product, we need to look for common factors among the terms within each product.

Let's start with the first product, (2x^2 + 5x)(7x - 14).

First, let's factor out any common factors from each term within the product.

For the first term, 2x^2 + 5x, we can factor out an x: x(2x + 5).

For the second term, 7x - 14, we can factor out a 7: 7(x - 2).

So, now our product becomes: x(2x + 5) * 7(x - 2).

To find the GCF, we need to identify the common factors between the two terms: (2x + 5) and (x - 2).

In this case, there are no common factors other than 1. So, the GCF of the first product is 1.

Moving on to the second product, (6y^2 - 3y)(y + 7).

Factoring out any common factors from each term within the product, we have:

For the first term, 6y^2 - 3y, we can factor out 3y: 3y(2y - 1).

For the second term, y + 7, there are no common factors to be factored out.

So, our product becomes: 3y(2y - 1)(y + 7).

To find the GCF, we need to identify common factors among the terms: (2y - 1) and (y + 7).

Again, in this case, there are no common factors other than 1. Therefore, the GCF of the second product is also 1.

In summary, the GCF of both products, (2x^2 + 5x)(7x - 14) and (6y^2 - 3y)(y + 7), is 1, as there are no common factors other than 1 between their terms.