Distribution learns to run in reverse. Factoring pulls the greatest common factor back out front, turning a sum into a product, and checking it is as easy as distributing again.
What you have to be able to do
Find the greatest common factor of numbers and of terms
Factor the GCF out of an expression
Check a factoring by distributing
The procedures
Finding the GCF
The GCF of the numbers is the largest number dividing them all.
For letters, take the smallest power of any letter every term shares.
The GCF of the terms is those two answers multiplied.
Factoring it out
Write the GCF out front.
Inside the parentheses, write what is left of each term after dividing by it.
No term ever vanishes: dividing a term by itself leaves 1, not nothing.
Checking
Distribute your answer back out.
It must rebuild the original expression exactly.
If it does not, the GCF was wrong or a leftover was.
Worked
WORKED
Factor 12x + 18. The GCF of 12 and 18 is 6. 12x divided by 6 is 2x; 18 divided by 6 is 3. ANSWER: 6(2x + 3)
WORKED
Factor 8x2 + 12x. The numbers share 4; both terms share one x. The GCF is 4x. 8x2 over 4x is 2x; 12x over 4x is 3. ANSWER: 4x(2x + 3)
Terms
Term
Meaning
factor
to rewrite as a multiplication
greatest common factor
the largest factor the terms share
prime number
a whole number greater than one whose only factors are one and itself
Check yourself
1. Find the GCF of 24 and 36
2. Factor: 5x + 20
3. Factor: 9x2 − 6x
reveal answers
12 · 5(x + 4) · 3x(3x − 2)
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 9, factoring foundationsalgebra 1 · oda