STANDARD 11:
FACTORING
The basics
Factoring: Pulling apart a polynomial (the opposite of multiplication)
Factors: are terms or polynomials that multiply together to make a larger polynomial or term
X-method: a method we use to visually organize the factoring process (only works for quadratic trinomials)
GCF: The Greatest Common Factor is the largest term (may be a number, a variable, or both) that can be divided out of every term in a polynomial. ** ***Always look for the GCF First!
Factors: are terms or polynomials that multiply together to make a larger polynomial or term
X-method: a method we use to visually organize the factoring process (only works for quadratic trinomials)
GCF: The Greatest Common Factor is the largest term (may be a number, a variable, or both) that can be divided out of every term in a polynomial. ** ***Always look for the GCF First!
Factoring Concept Map
The Greatest Common Factor
X-Method
In class, we used the x-method. There are other ways to factor as well (one example is in a video below).
How to use the x-method
1. Identify a, b, c
2. Put a*c on top of the x and the b-value on the bottom.
3. Find two numbers that have a product of the number on top, and a sum of the number on the bottom.
4. Write those numbers in factored form (x+ _) (x + _)
5. Check by distributing- you should get your original polynomial
How to use the x-method
1. Identify a, b, c
2. Put a*c on top of the x and the b-value on the bottom.
3. Find two numbers that have a product of the number on top, and a sum of the number on the bottom.
4. Write those numbers in factored form (x+ _) (x + _)
5. Check by distributing- you should get your original polynomial
X-Method when a does NOT equal one
When a does not equal one, we can still use the x-method, but there is an added step or two!
How to use the x-method when a does not equal one:
1. Identify a, b, c
2. Put a*c on top of the x and the b-value on the bottom.
3. Find two numbers that have a product of the number on top, and a sum of the number on the bottom- write them on the sides of the x
4. Divide both sides by the a-value to create fractions... reduce the fractions!
5. Create factors by putting an x next to the denominator and pushing the numerator off to the side
6. Check by distributing!
Check out another method to factoring here: http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factor-by-a-c-method.php
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