Factoring:

Algebra 2: Notes 4.3 & 4.4: GCF: The greatest common factor is the largest factor that divides all terms evenly.

5GCF x2 2 315 5 25

55 5 5

x y xy xx

x x x

2 2 315 5 25x y xy x

• Step 1: determine the GCF and write it down. Then divide each term by the GCF.

• Step 2: Simplify.

• Step 3: Check the result by using Distributive Property.

√

2 2 315 5 25x y xy x

2 25 3 5x xy y x

2 25 3 5 5 5x xy x y x x

Answer:

(4.3 & 4.4): Factor by Grouping(For polynomials with 4 or more terms)

Step 1: Change any subtract to add the opposite and Group the first 2 terms with parentheses and the last 2 terms.

Step 2: Take out a GCF for the 1st group, and for the 2nd group. Simplify.

Step 3: Factor out the common parentheses. Simplify.

Step 4: Check with FOIL

Pull out a -3 instead

3 22

2 2

3 2 9 63

3 3

x x xx

x x

3 23 2 9 6x x x

2 3 2 3 3 23 2

3 2 3 2

x x xx

x x

3 23 2 9 6x x x

2 3 2 3 3 2x x x

23 2 3x x 2 2

3 2

3 2 3 3 3 2

3 2 9 6

x x x x

x x x

√

Answer:

(4.3 & 4.4): Factoring Trinomials

• 3 ways to factor trinomials:– Area method– Guess and check method– Table method

(4.3 & 4.4): Factoring Trinomials: Area Method

• Step 1: Write the x2 term and the constant term in the diagonal rectangles.

• Step 2: Multiply down this diagonal.

• Step 3: Ask yourself, what two numbers can you multiply to get this and add to get the x term?

• Step 4: Write these numbers in the empty rectangles.

• Step 5: Factor the GCF out of each column and each row.

• Step 6: Check your factoring.

4x2

3

*=12x2 +=8x

1x*12x=12x2

2x*6x=12x2

3x*4x=12x2

1x*12x=13x

2x*6x=8x

3x*4x=7x

2x

6x

1

2x

2x 3

2x(2x)+2x(1)+3(2x)+3(1)=4x2+8x+3√

4x2+8x+3 = (2x+3)(2x+1)

(4.3 & 4.4): Factoring Trinomials: Guess & Check

• Step 1: Draw parentheses

• Step 2: Fill in the missing factors to get the first term.

• Step 3: Fill in the missing factors to get the last term.

• Step 4: Check by FOIL.

x2 + 10x + 25( )( )

(x )(x )

(x + 5)(x + 5)

x(x)+x(5)+5(x)+5(5)x2 + 10x + 25 √

(4.3 & 4.4): Factoring Trinomials: Table Method

• The Table Method incorporates both the Area Method and the Guess and Check Method.

Step 1: Draw parentheses4x2+15x+9

Step 2: Fill in the missing factors to get the first term.

Step 3: Fill in the missing factors to get the last term.

Step 4: Check by FOIL, if it doesn’t work retry steps 1 and 2.

=(4x+3)(x+3)

( )( )

( 2x )(2x ) or ( 4x )(1x )

( 2x )(2x ) or ( 4x )(1x )

+1 +9 +1 +9

+3 +3 +3 +3

( 4x +3)(1x+3)=4x(x)+4x(3)+3(x)+3(3)=4x2+15x+9√

(4.3 & 4.4): Factoring Formulas:

• Difference of Squares (only works for something squared

minus something squared)

• Sum of Cubes(only works for something cubed plus

something cubed)

• Difference of Cubes (only works for something cubed minus

something cubed)

• a2–b2=(a+b)(a–b)

• a3+b3=(a+b)(a2–ab+b2)

• a3–b3=(a–b)(a2+ab+b2)

(4.3 & 4.4): Summary of Factoring:

• Step 1: If all terms have a greatest common factor other than one, then factor is out.

• Step 2: If the polynomial has:– Four or more terms, then try the factoring by grouping

method.

– Three terms, then try the guess and check method.

– Two terms, then try factoring using the difference of squares method, sum of cubes method, or difference of cubes method.

(4.3 & 4.4): Solve by Factoring:

• Step 1: Factor the polynomial.• Step 2: Set each factor equal to zero and solve.

Example:22 21 0x x

2 7 3 0x x 2 7 0

7 7

2 7

2 27

2

x

x

x

3 0

3 3

3

x

x

73

2x or x

(4.3) √Points: Solve by Factoring:

(4.4) √Points: Solve by Factoring:

(4.3 & 4.4): Factoring Foldable Example:

(4.3) √Points: Solve by Factoring (answers):

(4.4) √Points: Solve by Factoring (answers):