Introduction:
GCF and LCM is one of the important and basic topics in mathematics. GCF is generally known as greatest common factor. For the given set of numbers, gcf is found by finding the factors of the given numbers. The common factors of a number are known as the gcf of the given numbers. Gcf of polynomials is defined as, finding the greatest factors for the given expression which consists of constants and variables in terms of exponents. Finding the gcf of polynomials is same as find the gcf of numbers. In addition to numbers, gcf of polynomials contains variables in it.
How to find the greatest common factor of polynomials:
The following are the steps to be followed when finding the gcf of polynomials,
Step 1: First find the common factors for the given numbers. A common factor is a number that divides both numbers evenly. Three is a common factor of 3 and 15.
Step 2: Next step is to find the gcf for the variables, then divide all of the numbers by their common factor.
Step 3: Continue this process with the resulting numbers until there are no more common factors for the given polynomial expression.
Step 4: The last step is to multiply all of the common factors of numbers and variables together to find the Greatest Common Factor of the given polynomial expression.
Example problems for finding the gcf of polynomials:
Example 1:
Find the gcf for the given polynomial expression, 2x ^2 + 4x.
Solution:
The gcf for the given expression,
2x ^2 = 2 * x *x
4x = 2*2*x
Here the common factors are,
= 2x
= 2x ( x + 2)
Here the gcf is 2x.
Example 2:
Find the gcf for the given polynomial expression, 3x3 + 18x ^2.
Solution:
The gcf for the given expression,
3x3 = 3 * x *x*x
18x ^2 = 3*3*2*x*x
Here the common factors are,
= 3*x*x
= 3x ^2
= 3x ^2 ( x + 6)
Here the gcf is 3x ^2.
Example 3:
Find the gcf for the given polynomial expression, 4x ^2 + 8x.
Solution:
The gcf for the given expression,
4x ^2 = 4 * x *x
8x = 4*2*x
Here the common factors are,
= 4*x
= 4x
= 4x ( x + 2)
Here the gcf is 4x.
GCF and LCM is one of the important and basic topics in mathematics. GCF is generally known as greatest common factor. For the given set of numbers, gcf is found by finding the factors of the given numbers. The common factors of a number are known as the gcf of the given numbers. Gcf of polynomials is defined as, finding the greatest factors for the given expression which consists of constants and variables in terms of exponents. Finding the gcf of polynomials is same as find the gcf of numbers. In addition to numbers, gcf of polynomials contains variables in it.
How to find the greatest common factor of polynomials:
The following are the steps to be followed when finding the gcf of polynomials,
Step 1: First find the common factors for the given numbers. A common factor is a number that divides both numbers evenly. Three is a common factor of 3 and 15.
Step 2: Next step is to find the gcf for the variables, then divide all of the numbers by their common factor.
Step 3: Continue this process with the resulting numbers until there are no more common factors for the given polynomial expression.
Step 4: The last step is to multiply all of the common factors of numbers and variables together to find the Greatest Common Factor of the given polynomial expression.
Example problems for finding the gcf of polynomials:
Example 1:
Find the gcf for the given polynomial expression, 2x ^2 + 4x.
Solution:
The gcf for the given expression,
2x ^2 = 2 * x *x
4x = 2*2*x
Here the common factors are,
= 2x
= 2x ( x + 2)
Here the gcf is 2x.
Example 2:
Find the gcf for the given polynomial expression, 3x3 + 18x ^2.
Solution:
The gcf for the given expression,
3x3 = 3 * x *x*x
18x ^2 = 3*3*2*x*x
Here the common factors are,
= 3*x*x
= 3x ^2
= 3x ^2 ( x + 6)
Here the gcf is 3x ^2.
Example 3:
Find the gcf for the given polynomial expression, 4x ^2 + 8x.
Solution:
The gcf for the given expression,
4x ^2 = 4 * x *x
8x = 4*2*x
Here the common factors are,
= 4*x
= 4x
= 4x ( x + 2)
Here the gcf is 4x.
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