WARM UP SOLVE USING THE QUADRATIC EQUATION, WHAT IS THE EXACT ANSWER. DON’T ROUND

WARM UP• SOLVE USING THE QUADRATIC EQUATION, WHAT IS THE

EXACT ANSWER. DON’T ROUND.

22 4 1x x 2( 4) ( 4) 4(2)(1)

2(2)

4 16 8

4

4 8

4

4 2 2

4

21

2

4 2 2

4 4

Factoring a polynomial means expressing it as a product of other polynomials.

THE GREAT THING ABOUT FACTORING

• YOU CAN ALWAYS CHECK YOUR YOU CAN ALWAYS CHECK YOUR

WORK. WORK.

• YOU CAN WORK BACKWARDS AND YOU CAN WORK BACKWARDS AND

MULTIPLY THE POLYNOMIALS TO MULTIPLY THE POLYNOMIALS TO

SEE IF YOUR ANSWER IS SEE IF YOUR ANSWER IS

CORRECT.CORRECT.

Factoring Methods:

1)GCF2)Difference of Squares3)Perfect Squares

4)Sum & Difference of Cubes5)Grouping (4 or more terms)

6)Trinomials

Day 1

Day 2

Day 3

Big Objective!

Factoring polynomials with a common monomial factor

(using GCF).

**Always look for a GCF before using any other factoring method.

Factoring Method #1

Steps:

1. Find the greatest common factor (GCF).

2. Divide the polynomial by the GCF. The quotient is the other factor.

3. Express the polynomial as the product of the quotient and the GCF.

3 2 2: 6 12 3Example c d c d cd

3GCF cdStep 1:

Step 2: Divide by GCF

(6c3d 12c2d2 3cd) 3cd

2c2 4cd 1

3cd(2c2 4cd 1)

The answer should look like this:

Ex: 6c3d 12c2d 2 3cd

GCF

T.O.O.

Factor these on your own looking for a GCF.

1. 6x3 3x2 12x

2. 5x2 10x 35

3. 16x3y4z 8x2 y2z3 12xy3z 2

23 2 4x x x

25 2 7x x

2 2 2 24 4 2 3xy z x y xz yz

GCF

Factoring polynomials that are a difference of squares.

Factoring Method #2

A “Difference of Squares” is a binomial (*2 terms only*) and it factors like this:

a2 b2 (a b)(a b)

To factor, express each term as a square of a monomial then apply the rule... a2 b2 (a b)(a b)

Ex: x2 16 x2 42

(x 4)(x 4)

Here is another example:

1

49x2 81

1

7x

2

92 1

7x 9

1

7x 9

Try these on your own:

1. x 2 121

2. 9y2 169x2

3. x4 16

Be careful!

11 11x x

3 13 3 13y x y x

22 2 4x x x

IS IT A DIFFERENCE OF SQUARES?IF SO… FACTOR IT.

1) X2 – 4

2) 9X2 – 1

3) 2X2 – 4

4) 2X2 – 8

5) X2 + Y2

6) X3 – 25

7) 9XY – Y2

8) -16 + X2

9) -4 – 16X2

10) X4 – 81

1) YES -------------- (X+2)(X-2)

2) YES -------------- (3X+1)(3X-1)

3) NO √2

4) YES 2(X2 – 4) -2(X+2)(X-2)

5) NO ADDING

6) NO X3

7) NO √ XY

8) YES X2 – 16 ---(X+4)(X-4)

9) NO -(4 + 16X2) -(16X2 + 4)

10) YES √X4 = X2 ---(X2+2)(X2-2)

Factoring Method #3

Factoring a perfect square trinomial in the form:

a2 2ab b2 (a b)2

a2 2ab b2 (a b)2

Perfect Square Trinomials can be factored just like other trinomials (guess and check), but if you recognize the perfect squares pattern, follow the formula!

a2 2ab b2 (a b)2

a2 2ab b2 (a b)2

Ex: x2 8x 16

x2 8x 16 x 4 2

2

x 2 4 2

Does the middle term fit the pattern, 2ab?

Yes, the factors are (a + b)2 :

b

4

a

x 8x

Ex: 4x2 12x 9

4x 2 12x 9 2x 3 2

2

2x 23 2

Does the middle term fit the pattern, 2ab?

Yes, the factors are (a - b)2 :

b

3

a

2x 12x

T.O.O: IS IT A PERFECT SQUARE TRINOMIAL?

1) X2 + 8X + 16

2) X2 + 6X – 9

3) X2 + 5X + 25

4) X2 + 10X + 25

5) 4X2 – 20X + 25

6) X2 + 8X + 12

7) 49 – 14Y + Y2

8) 2X2 + 8X + 16

9) X2 – 2X – 3

10) X2 – 2X + 1

HOMEWORK

•FACTORING WS #1FACTORING WS #1