Algebra I - A Verbose Approach/Factoring
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This is a review of factoring numbers.
Contents |
[edit] Factors
A factor of a number is any two numbers that can be multiplied together to make the number we are factoring. An example a factor of the number 16 is (8 and 2) because 8 * 2 = 16. Here is a list of all of 16's factors: (1 and 16), (2 and 8), and (4 and 4).
[edit] Divide Evenly
Before we start factoring we need to learn a dictionary term: divide evenly. Divide evenly means that when you divide two numbers together there isn't a remainder or there is a remainder of zero (how ever you want to say it). 2 divides evenly into 4 because 2 divided by 4 is 2. 3 does not divide evenly into 14 because 3 divided by 14 is 4 with a remainder of 2.
[edit] Possible Factors
To factor we must first look for possible factors. Possible factors are any number that might be a factor. Once we have a possible factor then we divide that number into the number we are factoring. If they divide evenly then we have a factor! The factor is the possible factor we found and the result of the division problem. Here is an example. Let's say the number we are factoring is 20. 2 is the possible factor. 20 / 2 = 10. They divide evenly which means we have a factor. The factors are 2 (the possible factor), and 10 (the result of the division problem). Now that we have a factor we start over with a new possible factor and find all of the factors.
The possible factors for any number are every number between one and itself. For example the factors for 12 are: 1,2,3,4,5,6,7,8,9,10,11, and 12. Try every factor in order starting at one. Lets factor some numbers
[edit] Examples
Factor 12
First find all the possible factors
The possible factors are 1,2,3,4,5,6,7,8,9,10,11, and 12
next we will try them one by one
12/1 = 12 (1 and 12 are factors)
12/2 = 6 (2 and 6 are factors)
12/3 = 4 (3 and 4 are factors)
12/4 = 3 (we already have the factors 3 and 4)
Once we get a factor we already have then we know we have all the factors.
So the factors for 12 are (1 and 12), (2 and 6), and (3 and 4)
Factor 54
First find all the possible factors
The possible factors are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, and 54
Do not worry this is not as much work as it seems!
54/1 = 54 (1 and 54 are factors)
54/2 = 27 (2 and 27 are factors)
54/3 = 18 (3 and 18 are factors)
54/4 = 13r2 (4 is not a factor)
54/5 = 10r4 (5 is not a factor)
54/6 = 9 (6 and 9 are factors)
54/7 = 7r5 (7 is not a factor)
54/8 = 6r6 (8 is not a factor)
54/9 = 6 (we already have the factors 9 and 6)
See that was easy.
So the factors for 54 are (1 and 54), (2 and 27), (3 and 18), and (6 and 9)
[edit] Factoring Algebric Expressions
We can use this knowledge of factoring numbers to factor algebric expressions, we will use both momonials and polynomials.
A momoninal is a expression with only 1 term.
Example: 3x2y.
A polynomial is an expression with 2 or more terms.
Example: 4x3+2x2+7
