Introduction
This website is a good way to learn how to factor polynomials in many different ways. Learning how to use these different methods can help solve these problems so much faster.
Task
GCF Factoring
To factor using Greatest Common Factor method you have to figure out the biggest number that will go into both number. For example, 30 and 20 would have a GCF of 5.
Example: 8x - 16y
1. First take the GCF out of both: 8
2.Factor: 8 (x -2y)
3. What you just factored is your answer:8 (x -2y)
Process
Factoring By Grouping
Factoring by grouping is when you take the factor and group the numbers that are simular. An example would be 6 +3 +15x + 5x2.
Example: 6 +3 +15x +5x2
1: Put parentheses around the two groups: (6 +3 )+(15x + 5x2)
2: Now factor each one seperatly :9+3 15x + 5x2
3 (3 + 1) 5x ( 3 + x)
3. Now, since the problem is positive, you add the the 3 and the 5x: (3 + 5x)
4. You now have the same thing in the other set of parenthese which you will keep the same: (3 + x)
5. Finally you multiply the two sets of parenthese: (3 + 5x) (3 + x) And that's your answer.
Evaluation
Basic Trinomials
Basic trinomials are where you factor the number without the variable and get the factors that equal the number in the middle (#x).
Example: x2 + 10x + 16
1. Take the 16 and factor it down. 16
16 1= 17
8 2= 10
4 4=8
2. After it's been factored then you find the numbers that add up to the middle number: 8,2
3. Now you will take the factors that add up and you put them in a different set of parenteses. Each set will start with an x: (x + 8) (x + 2)
4. Now you can check that answer if you want by foiling it.
5. When your signs are differnent:
a b equation sign
+ + x2 + #x + # +
_ + x2 - #x + # _
_ _ x2 - #x -# (x + Lg#)(x - Sm#)
+ _ x2 + #x -# (x + Sm#)(x - Lg#)
Conclusion
Harder Trinomials
A hard trinomial is set up exactly alike a basic trinomial but this time theres a number in front of the x2.
Example: 2x2 + 15x + 7
1. Multiply the first number by the last number: 2•7=14
2. Factor the product: 14
14 1=15
7 2=9
3. Add, or subtract, the numbers until you find the two that add up to the number in the middle with the x.
4.Take the factors and put them with the approprite number. The numbers you put them with are the ones you multiplied in the beginning: (2x2 + 2)+( 7 + 7)
5. No you factor them using the Grouping method: 2x(x + 1) 7 (1 + 1)
(2x +7) (x + 1)
(2x +7) (x + 1) Is your final answer. To check it you can foil it out and also to make sure your signs are right look back at the chart.
Credits
Special Factoring
Special factoring is when the two numbers you are factoring are perfect squares. For example, 3 is the perfect square of 9 and 9 is the perfect square of 81.
Example: 16x4 - 25
1. Split the first number itnto it its perfect square and put into two sets of parenthese, one positive,+, and one negative,-: (4x2 + ?) (4x2 - ?)
2. Now you do the same to the other number but you put it in the sets of parenathese with the other perfect square: (4x2 + 5) (4x2 - 5), that's your answer.