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.