Finding the Greatest Common Factor of Polynomials
In a multiplication problem, the numbers multiplied together are called factors. The answer to a
multiplication problem is called the product.
In the multiplication problem , 5 and 4 are factors and 20 is the product.
If we reverse the problem, , we say we have factored 20 into .
In this worksheet we will factor polynomials.
In the multiplication problem ( ) , are the factors and is the product.
If we reverse the problem, ( ) , we say we have factored into .
Name the factors and the product in each problem.
1. ( ) factors: __________________________ product: __________________
2. ( ) factors: __________________________ product: __________________
3. ( ) factors: __________________________ product: __________________
4. ( ) factors: __________________________ product: __________________
The first step in factoring polynomials is to factor out the greatest common
factor (GCF). This is the largest integer and highest degree of each variable
that will divide evenly into each term of the polynomial.
Factoring is the reverse of multiplying!
In the polynomial , 5 is the largest integer that will divide 5x and 35, and we cannot factor out
any variable because the second term, 35, does not have a variable part.
To factor we write: ( ) .
In the polynomial , 3 is the largest integer that will divide . We can factor out
because each term has at least one factor of (look for the term with the lowest degree of each
variable).
To factor we write: ( ).
In the polynomial , 4 is the largest integer that will divide . We can factor
out and because each term has at least one factor of and two factors of .
To factor we write: ( ).
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