INTRODUCTION TO FACTORING POLYNOMIALS
MSJC ~ San Jacinto Campus
Math Center Workshop Series
Recall: Factors of a number are the numbers that divide the original number evenly.
Writing a number as a product of factors is called a factorization of the number.
The prime factorization of a number is the factorization of that number written as a product of prime numbers.
Common factors are factors that two or more numbers have in common.
The Greatest Common Factor (GCF) is the largest common factor.
Ex: Find the GCF(24, 40).
Prime factor each number:
24 = 2*2*2*3 = 23*3
40 = 2*2*2*5 = 23*5
= 23 = 8
The Greatest Common Factor of terms of a polynomial is the largest factor that the original terms share
Ex: What is the GCF(7x2, 3x)
7x2 = 7 * x * x
3x = 3 * x
The terms share a factor of x
GCF(7x2, 3x) = x
Ex: Find the GCF(6a5,3a3,2a2)
6a5 = 2*3*a*a*a*a*a
3a3 = 3*a*a*a
2a2 = 2*a*a
The terms share two factors of a
Note: The exponent of the variable in the GCF is the smallest exponent of that variable the terms
To factor an expression means to write an equivalent expression that is a product
To factor a polynomial means to write the polynomial as a product of other polynomials
A factor that cannot be factored further is said to be a prime factor (prime polynomial)
A polynomial is factored completely if it is written as a product of prime polynomials
To factor a polynomial completely, ask
Do the terms have a common factor (GCF)?
Does the polynomial have four terms?
Is the polynomial a special one?
Is the polynomial a difference of squares?
a2 – b2
Is the polynomial a sum/difference of cubes?
a3 + b3 or a3 – b3
Is the trinomial a perfect-square trinomial?
a2 + 2ab + b2 or a2 – 2ab + b2
Is the trinomial a product of two binomials?
Ex: Factor 7x2 + 3x