Factoring To Turn To Factored From

 

Standered form equation: y=ax2+bx+c

 

Common Factoring

 

-When common factoring you find the common numbers and variables in the expression

 

Example: 2x3+8x2

 

Step 1:Find out whats common

2x3+8x2

-The number 2 and 8 have somthing in common, they can both be multiples of 2.

 

Step 2:Factor whats common and put it outside the bracket

2(x3+4x2)

 

Step 3:Factor anything else that can be factored out

2(x3+4x2)

2x(x2+4x)

2xx(x+4)

2x2(x+4)

 

Fianl answer=2x2(x+4)

 

 

Simple Trinomial

 

Trinomial-ax2+bx+c

-A simple trinomial has no coefficient in the begining which means theres a coefficient

 of 1 only.

 

Example: x2+5x+6

 

What are you looking for?

-You are finding what two things multiplied together to form this equation

x2+5x+6=(?)(?)

 

Step 1:Find the factors of the "c" value

x2+5x+6

Factors of 6: 1x6

                     2x3

                     3x2

 

Step 2:From the factors found for the "c" value pick the factors that add up to the "b" value

x2+5x+6

Factors of 6 that add up to 5: 2x3

                                               3x2

 

Step 3:Try out the factors and see if they form your equation by expanding

x2+5x+6=(?)(?)

x2+5x+6=(x+3)(x+2)

Final answer-(x+3)(x+2)

 

 

Complex Trinomials

-Complex trinomials are trinomials which starts with a coefficient not equal to 1

 

Complex to Simple

-You can turn a complex trinomial to a simple trinomial by finding common factors

 

Example:3x2-6x+9(complex)

 

Step 1: Factor out whats common

3(x2-2+3)(simple)

 

Step 2:Now that that its a simple trinomial use your skill with simple trinomials to figure out the answer

3(x2-2+3)

Factors of 3: 1x3

                     3x1

                    -1x3

                    1x-3

 

Step 3: Use the factors that multiply to "c" value but also add up to "b" value

3(x2-2+3)

=(x+1)(x-3)

 

 

But...

 

Not all the time do complex trinomials turn into simple trinomials. This is when there is nothing common.

 

So..

 

Use guess and check method 

 

 

Perfect Squares

 

Step 1:Sqaure the "a" and "c" value in you equation

 

Example 4x2+12x+9

√4=2

√9=3

 

Step 2:Once you sqaure rooted make sure its correct by multiplying the two numbers you sqaure rooted together then multiply wiht 2

 

4x2+12x+9

 

√4=2

√9=3

2x3x2

=12

 

Step 4:If you multipied the two numbers you got after sqaure rooting with two and ended up with your "b" term then you did it correctly and could move onto the next step

 

Step 5:Make the equation

 

4x2+12x+9

√4=2

√9=3

(2x+3)(2x+3)

(2x+3)2

 

You know its a perfext square when you end up with two brackets with the same numbers in them

 

 

Difference of Square

 

Differnce of aqaure only has two numbers.These numbers can both be sqaured by two differnt numbers.

 

Step 1:Square root both your numbers

 

Example: 16x2-25

√16=4

√25=5

 

Step 2:Make your equation

16x2-25

√16=4

√25=5

(4x-5)(4x+5)

 

This is a difference of aqaure because the last term is negative, if it were a poistive it would be a perfect sqare.That is why the final results come with one positve and one negative number in both brackets.