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

3 ways to factor trinomials: (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 4x2+8x+3 = (2x+3)(2x+1) 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. 1 2x 3 4x2 2x 6x 3 *=12x2 +=8x 1x*12x=12x2 2x*6x=12x2 3x*4x=12x2 1x*12x=13x 2x*6x=8x 3x*4x=7x 2x(2x)+2x(1)+3(2x)+3(1)=4x2+8x+3√

x2 + 10x + 25 ( )( ) (x )(x ) (x + 5)(x + 5) x(x)+x(5)+5(x)+5(5) (4.3 & 4.4): Factoring Trinomials: Guess & Check x2 + 10x + 25 ( )( ) (x )(x ) (x + 5)(x + 5) x(x)+x(5)+5(x)+5(5) x2 + 10x + 25 √ 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.

(4.3 & 4.4): Factoring Trinomials: Table Method The Table Method incorporates both the Area Method and the Guess and Check Method. 4x2+15x+9 =(4x+3)(x+3) Step 1: Draw parentheses ( )( ) Step 2: Fill in the missing factors to get the first term. ( 2x )(2x ) or ( 4x )(1x ) Step 3: Fill in the missing factors to get the last term. ( 2x )(2x ) or ( 4x )(1x ) +1 +9 +1 +9 +3 +3 +3 +3 Step 4: Check by FOIL, if it doesn’t work retry steps 1 and 2. ( 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)

Step 2: If the polynomial has: (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.

Step 1: Factor the polynomial. (4.3 & 4.4): Solve by Factoring: Step 1: Factor the polynomial. Step 2: Set each factor equal to zero and solve. Example:

(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):