Factori ng: Algebra 2: Notes 4.3 & 4.4: GCF : The greatest common factor is the largest factor that divides all terms evenly. 5 GCF x 2 2 3 15 5 25 5 5 5 5 xy xy x x x x x 2 2 3 15 5 25 xy 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 3 15 5 25 xy xy x 2 2 5 3 5 x xy y x 2 2 5 3 5 5 5 x xy xy x x Answer:
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Factoring: Algebra 2: Notes 4.3 & 4.4: GCF: The greatest common factor is the largest factor that divides all terms evenly. Step 1: determine the GCF and.
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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.