In order to excel in factoring algebraic expressions, we must completely understand the concept of the greatest common factor (GCF). Remember that any integer can be written as a product of prime numbers, and the GCF of two or more numbers is the greatest integer factor of each number.
The Greatest Monomial Factor
The concept of greatest common factor of basic counting numbers can be extended to monomials and polynomials. We know that the greatest common factor (GCF) is thelargest number that divides each number in a given set. As this concept is extended to monomials and polynomials, GCF is described below.
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By identifying the GCF, a polynomial can be written into its factored form. To determine the factored form of a polynomial, perform the following steps:
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Grouping Terms with a Common Factor
Let us consider the polynomial below. (i) ab + bc + ad + cd Does the polynomial have a common factor for each of its terms? No, it does not have any GCF aside from 1, which could make us think that this polynomial is not factorable anymore. But before concluding so, let us rewrite this polynomial first by grouping its terms that have a common factor. We will have the following as possible groupings.
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