ALGEBRA II

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Factoring: Why bother?makes a polynomial simpler

helps to find the zeros (x-intercepts, solutions)

because it’s so much fun!!!

An expression may be :

factored over the set of integers

irreducible over the integers (not factorable with real numbers)

Greatest Common Factor: expression of the highest degree that divides each term of the polynomial

Bain’s Words for GCF: one of every unique factor to the highest degree that it occurs!

Guided Practice Factoring using GCF:

3 21. 18 27x x 22. ( 3) 5( 3)x x x

Factoring by Grouping: group terms together that have a common factor

Guided Practice: 3 21. 4 3 12x x x

3 22. 5 2 10x x x

Factoring Trinomials: may be done by a variety of different methods – guess and test, grouping (5-step method).Refresher on 5-step method1. ac

2. factors of ac that add or subtract to give the middle term

3. rewrite middle term using the factors

4. group

5. factor!

Example:

2ax bx c

2 13 40x x

Guided Practice: Factor the trinomials…

Factoring a trinomial in 2 variables:

21. 5 14x x 22. 8 10 3x x

2 21. 2 7 3x xy y 2 22. 3 13 4 (5-step method)x xy y

Factoring the difference of 2 squares:2 2 ( )( )a b a b a b

21. 4x 22. 81 49x

43. 81x

Factoring Perfect Square Trinomials:

Guided Practice:

2 2 2

2 2 2

2 ( )

2 ( )

a ab b a b

a ab b a b

21. 6 9x x 22. 25 60 36x x

Factoring the Sum/Difference of 2 cubes:

Guided Practice:

3 3 2 2

3 3 2 2

( )( )

( )( )

a b a b a ab b

a b a b a ab b

31. 8x 32. 64 125x

Whiteboard Practice:Factor out the gcf:

Factor by grouping:

Factor:

21. 4x 8x 2. x(2x+1)+4(2x+1)

3 21. x 3 4 12x x 3 22. x 6 2 12x x

21. 6x 17 12x 22. 15x 19 6x 2 23. 36 49x y 24. x 10 25x

35. 5x 45x