By Gurshan Saran

FACTORING FLOW CHART

FACTORING

Now check, how many terms?Afterward, ask yourself, Is there a GCF?

The first thing you should always do if it has not been done is: Put it in proper order ( 3x2+ 9x + 12)

Yes?

How to Factor Out an GCF1. Find a greatest common factor for all of

the terms

2. Prime Factor and take all of the common bases with the lowest exponent

**Also note that if the 1st term is negative, we should factor out a negative with the GCF

3. Divide each term by the GCF and put it inside the brackets. Write the GCF outside of

the brackets set

Example

-3x3 - 15xy

Common base = -3, Lowest exponent = x

-3x( -3x3

-------- + -3x

15xy )-------3x

= -3x (x2 +3y)

NO?

2 TERMS ?

Difference of Squares 2 - 2

3 TERMS ? 4 TERMS ?

Easy Quadratic? 1x2 + 4x + 8

Hard Quadratic?(3x2 + 54x + 21)

Decomposition

Factoring By Grouping

4x2 + 4x + 8x + 2

Difference of Squares FactoringThey have 2 terms that are perfect squares and are subtracted!

1. Draw 2 sets of brackets

2. Take the square root of both terms and put in both brackets

3. Separate with a + in one and a – in the other

Example:

Factor: 9x2 – 16y2

( ) ( )

(3x 4y) (3x 4y)

(3x+4y) (3x-4y)

Factoring Easy Quadratics (a=1)

1. Now, look at the last term and the middle term and think what 2 numbers multiply to get the last term and add to get the middle term

2. Now, draw a set of brackets

3. Put an x in each bracket and then just simply put those values that you found

Example: Factor x2 + 10x + 16

Lets try 8 & 2. 8 x 2 = 16 (our last term) and 8 + 2 = 10 (our middle term) It works!

( ) ( )

(x+2) (x+8)

Factoring Hard Quadratics (a 1)In this example, I am using the decomposition method

1. Multiply the 1st term and the last term and get a product

2. Find 2 numbers that multiply to this product and add to the middle term

3. Replace the middle term with those 2 terms

4. Now we can easily factor this by grouping

Example:Factor 6x2 + 11x + 4

Product = 24

Two numbers that multiply to 24 and add to 11 are 8 & 3

= 6x2 + 3x + 8x + 4

2(3x+4) +1(3x+4)

=(2x+1)(3x+4)

Factoring By Grouping (4 term expressions)

1. Here we have 4 terms. First factor the first 2 terms and the last 2 terms.

2. Now you can check if you did this right because both brackets should be the same.

3. Now you can group together the terms outside the brackets and then all you are left with is the common factor that’s in the brackets. Now this becomes a FOIL type question and it is done

Example: Factor 2x2 + 4x + 6x + 12

2x(x+2) +6(x+2)

(2x+6) (x+2)

Once you are finished ANY factoring problem, you can check it by using FOIL and multiplying out the brackets. Thanks for watching!