Factoring is the process of transforming an expression into a product of factors. For instance, 15 can be written as (5)(3), with 5 and 3 referred to as factors of 15. Polynomial expressions can also be used in this way.
The GCF must be a factor of each term, which means that the GCF must divide all the terms. Within an algebraic equation, a monomial is a single term. It could be a number, a variable, or a combination of both.
This should also be the initial step when factoring in general, as it will usually simplify the problem.
To employ this method, we simply examine all of the terms to determine whether there is a factor that appears in each of them. If it exists, we'll factor it out of the polynomial.
It's also worth noting that in this case, we're merely implementing the distributive law backwards.
Note: The Greatest Common Monomial Factor (GCMF) must be a factor of EVERY polynomial term.
Steps in Getting the Greatest Common Monomial Factor (GCMF):
Step 1)Look at the coefficients.
A coefficient is a numerical or constant amount added before and multiplied by the variable in an algebraic expression.
Given our polynomial expression:
Our coefficients are: 14, 21, and 28
Listing the factors of each coefficient:
14: (1, 2, 7, 14)
21: (1, 3, 7, 21)
28: (1, 2, 4, 7, 14, 28)
Thus, the greatest common factor of 14, 21, and 28 is 7.
Step 2)Look at the variables.
In algebra, a symbol (usually a letter) represents an unknown numerical value in an equation.
There are three variables in the polynomial expression: x, y, and z.
How to get the greatest common factor of variables?
Answer: You can simply pick the variable with the lowest exponent.
In variable x:
The variable with the lowest exponent is
In variable y:
Again, the one with the lowest exponent is
In variable z:
The one with the lowest exponent is
Step 3)Determine the GCF.
The Greatest Common Factor (GCF) is
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Some important notes:
Factoring polynomials can be done in six different ways. The following are the six methods:
Greatest Common Factor (GCF)
Grouping Method
Sum or difference in two cubes
Difference in two squares method
General trinomials
Trinomial method
While it is critical for students to achieve procedural fluency in finding the greatest common factors, it is also critical to know that finding GCF is a foundation ability required for more complex applications in the future. It is also helpful to learn procedural fluency when dealing with algebraic manipulations and fractions operations in higher grades.
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Answer:
The Greatest Common Factor (GCF) is
.
Step-by-step explanation:
GREATEST COMMON MONOMIAL FACTOR
Factoring is the process of transforming an expression into a product of factors. For instance, 15 can be written as (5)(3), with 5 and 3 referred to as factors of 15. Polynomial expressions can also be used in this way.
Note: The Greatest Common Monomial Factor (GCMF) must be a factor of EVERY polynomial term.
Steps in Getting the Greatest Common Monomial Factor (GCMF):
Step 1) Look at the coefficients.
Given our polynomial expression:
Our coefficients are: 14, 21, and 28
Listing the factors of each coefficient:
Thus, the greatest common factor of 14, 21, and 28 is 7.
Step 2) Look at the variables.
How to get the greatest common factor of variables?
Answer: You can simply pick the variable with the lowest exponent.
In variable x:
In variable y:
In variable z:
Step 3) Determine the GCF.
The Greatest Common Factor (GCF) is
------
Some important notes:
Factoring polynomials can be done in six different ways. The following are the six methods:
While it is critical for students to achieve procedural fluency in finding the greatest common factors, it is also critical to know that finding GCF is a foundation ability required for more complex applications in the future. It is also helpful to learn procedural fluency when dealing with algebraic manipulations and fractions operations in higher grades.
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