1. There are several methods for factoring polynomials outlined in the document: factoring using the distributive property, factoring the difference of two squares/cubes, factoring a perfect square trinomial, and factoring general trinomials using trial and error or grouping. 2. Factoring trinomials involves determining the signs in the factors based on the signs of the terms, then finding two factors of the constant term that satisfy the middle term. 3. More complex polynomials can be factored by grouping like terms or using special factoring patterns like the difference of squares/cubes.

1. Factoring Polynomials
1. Factoring Using the Distributive Prop
2. Difference of Two Squares
3. Difference of Two Cubes
4. Sum of Two Cubes
5. Trinomials
6. Grouping

2. Factoring Polynomials
D is trib u tiv e P ro p e rty
C a n yo u divid e a ll term s b y the
sa m e nu m be r or lette r?
2 term s 3 term s 4 term s
D iffere nc e of 2 s q ua res P e rfe c t S q ua re? G rou ping
D iffere n ce of 2 cu b es T rial a nd Error
S u m o f 2 cu b es

3. Distributive Property
5x2y3 – 15x3y + 25x2y
5x2y(y2 – 3x + 5)

4. 2 Terms
Difference of Squares
4x2 – 9y6
(2x – 3y3)(2x + 3y3)

5. 2 Terms
Difference of Cubes
– 8x 3 27y 6
(2x – 3y2)(4x2 + 6xy2 + 9y4)
First Factor Second Factor - Use first factor
cube root of each term 1. Square 1st term
same sign 2. Change sign
3. Multiply the 2 terms
4. Square 2nd term (always +)

6. 2 Terms
Sum of Cubes
+ 8x 3 27y 6
(2x + 3y2)(4x2 - 6xy2 + 9y4)
First Factor Second Factor - Use first factor
cube root of each term 1. Square 1st term
same sign 2. Change sign
3. Multiply the 2 terms
4. Square 2nd term (always +)

7. 3 Terms
Perfect Square
4x 2 – 20x + 25
(2x - 5)2
* The first and last term must be perfect squares
a. Exponents have to be even to be perfect squares
1. Take the square root of the first term
2. Take the first sign
3. Take the square root of the last term.
4. Check: the middle term should be 2 times the first term
times second term

9. Factoring Trinomials
When the leading coefficient
is 1

10. Factoring Trinomials
1. Make sure trinomial is in
descending order of variable.
Divide out any common
factors.
Example:
x 2 + 5x + 6

11. Factoring Trinomials
2. Start out with two sets of
parentheses. These are the
factors.
Example:
x 2 + 5x + 6
( )( )

12. Factoring Trinomials
3. Put the variable given at the
beginning of each factor
Example:
x2 + 5x + 6
( x )( x )

13. Factoring Trinomials
4A. Determine signs in factors.
a) Since the last sign is + the
signs are the same
b) Since the first sign is + they
are both +
x 2 + 5x + 6
( x + )( x + )

14. Factoring Trinomials
4A. Find two factors of the last
number that add up to the
middle number.
Example:
x 2 + 5x + 6
( x + 3 )( x + 2 )

15. Factoring Trinomials
4B. Determine signs in factors.
a) Since the last sign is + the
signs are the same
b) Since the first sign is - they
are both +
x2 - 5x + 6
( x - )( x - )

16. Factoring Trinomials
4B. Find two factors of the last
number that add up to the
middle number.
Example:
x 2 - 5x + 6
( x - 3 )( x - 2 )

17. Factoring Trinomials
4C. Determine signs in factors.
a) Since the last sign is - the
signs are different
b) Since the first sign is + the
bigger number goes by the +
x 2 + 5x - 6
( x + )( x - )

18. Factoring Trinomials
4C. Find two factors of the last
number whose difference is
the middle number.
Example:
x 2 + 5x - 6
( x + 6 )( x - 1 )

19. Factoring Trinomials
4D. Determine signs in factors.
a) Since the last sign is - the
signs are different
b) Since the first sign is - the
bigger number goes by the +
x 2 - 5x - 6
( x + )( x - )

20. Factoring Trinomials
4D. Find two factors of the last
number whose difference is the
middle number.
Example:
x2 - 5x - 6
( x + 1 )( x - 6 )

21. 3 Terms
Trial and Error (FOIL)
6x – 11x + 4
2
(2x - 1)(3x - 4)
Signs:
1. If last sign is + then both factors have the same sign
a. If the first sign is + both factors have + sign
b. If the first sign is – both factors have - sign
2. If last sign is – then both factors have different signs

22. 4 Terms
Grouping
x3 – 4x2 + 3x - 12
x 2(x - 4) + 3(x - 4)
(x – 4)(x2 + 3)