Question

Factor the expression using the GCF 75m+85

Answer 1

General Idea:

To find the Greatest Common Factor of binomial, we need to write each term as product of prime factors. GCF by definition means the product of common prime factors involved with its lowest terms. It is a number which will go in to both the terms in a binomial.

Given :

$75m + 85$

Applying the concept :

$75m=3 \; \times \; 5^2 \; \times m\\\\85=5 \; \times \; 17\\\\GCF\; of\; 75m + 85 \;is\; 5$

In order to get the expression inside the parenthesis after factoring GCF 5, we need to divide each term by what we factor out as shown below:

$75m+85=5( \frac{75m}{5} + \frac{85}{5} )=5(15m+17)$

Answer 2

75m + 85 = 5(15m + 17)