1. 4.4 Factoring Polynomials
Objective
• review factoring quadratics
• factor by grouping.
• factor perfect square binomials
• factor difference of squares
• factor difference of cubes
• factor sum of cubes

2. Factoring Chart This chart will help you to determine which method of factoring to use Type Number of Terms
1. GCF or more
2. Diff. Of Squares 2
Trinomials 3
Sum-diff of cubes 2

3. Concept: Review Factoring Trinomials
Factor. 3x2 + 14x + 8
This time, the x2 term DOES have a coefficient (other than 1)!
Step 1: Multiply 3 • 8 = 24 (the leading coefficient & constant).
24 = 1 • 24
= 2 • 12
= 3 • 8
= 4 • 6
Step 2: List all pairs of numbers that multiply to equal that product, 24.
Step 3: Which pair adds up to 14?

4. Concept: Factoring Trinomials cont…
Factor. 3x2 + 14x + 8
Step 4: Write temporary factors with the two numbers.
( x )( x ) 2 12 3 3
Step 5: Put the original leading coefficient (3) under both numbers. 4 2
( x )( x ) 12 3
Step 6: Reduce the fractions, if possible. 2
( x )( x ) 4 3
( 3x + 2 )( x + 4 )
Step 7: Move denominators in front of x.

5. Concept: Factoring Trinomials cont…
Factor. 3x2 + 14x + 8
You should always check the factors by distributing, especially since this process has more than a couple of steps.
( 3x + 2 )( x + 4 )
= 3x • x + 3x • • x + 2 • 4
= 3x x + 8 √
3x2 + 14x + 8 = (3x + 2)(x + 4)

6. Concept: You Try
Factor: 2x2 + 11x + 12
Answer: (2x + 3)(x + 4)

7. Concept: Difference of Squares
Given: (Ax2 – B) where all given terms are perfect squares, you can quickly factor the binomial as follows: (Ax2 – B) = (√Ax2 + √B) (√Ax2 – √B) Ex: 9x2 – 25 (√9x2 + √25) (√9x2 – √25)
( ) ( ) 3x + 5 3x – 5

8. Concept: You Try!!!
16x2 – 4
Answer: (4x + 2)(4x – 2)

9. Concept: Factoring By Grouping
Given a polynomial in the form: ax3 + bx2 + cx + d
Check to see if you can factor out a common term
Group in pairs so they have a common factor.
2x4 + 8x3 – 18x2 – 72x
2x x x x
2x[x3 + 4x2 – 9x –36]
2x[(x3 + 4x2) + (– 9x –36)]

10. Concept: Factoring Other Powers
2x[(x3 + 4x2) + (– 9x –36)]
factor: x –9
2x[ x2(x + 4) –9(x + 4) ]
2x(x2 – 9)(x + 4)
3) Factor out the
common term from
each group.
Notice the green ( ) are the same. Write as two groupings.

11. Concept: Factoring Other Powers
2x (x2 – 9)(x + 4)
(x2 – 9) is a difference of squares and will factor apart.
(x2 – 9)
(x + 3)(x – 3)
Answer:
2x(x + 3)(x – 3)(x + 4)
Check to see if either
of the two sets of ( )
will factor any further.
6) Write all of the factors.

12. Concept: You Try Factor: 3x3 + 6x2 – 3x – 6 2) 4x3 + 4x2 + 28x + 28
Answers:
3(x+1)(x–1)(x+2) (x2 + 7)(x+1)
Note: this is not a
difference of
squares