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

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

THE GREAT THING ABOUT FACTORING YOU CAN ALWAYS CHECK YOUR WORK. YOU CAN ALWAYS CHECK YOUR WORK. YOU CAN WORK BACKWARDS AND MULTIPLY THE POLYNOMIALS TO SEE IF YOUR ANSWER IS CORRECT. YOU CAN WORK BACKWARDS AND MULTIPLY THE POLYNOMIALS TO SEE IF YOUR ANSWER IS CORRECT.

Factoring Methods: 1)GCF 2)Difference of Squares 3)Perfect Squares 4)Sum & Difference of Cubes 5)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.

Step 1: Step 2: Divide by GCF

The answer should look like this: GCF

T.O.O. Factor these on your own looking for a GCF. 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:

To factor, express each term as a square of a monomial then apply the rule...

Here is another example:

Try these on your own:

IS IT A DIFFERENCE OF SQUARES? IF SO… FACTOR IT. 1)X 2 – 4 2)9X 2 – 1 3)2X 2 – 4 4)2X 2 – 8 5)X 2 + Y 2 6)X 3 – 25 7)9XY – Y 2 8)-16 + X 2 9)-4 – 16X 2 10)X 4 – 81 1)YES  (X+2)(X-2) 2)YES  (3X+1)(3X-1) 3)NO √2 4)YES 2(X 2 – 4) -  2(X+2)(X-2) 5)NO ADDING 6)NO X 3 7)NO √ XY 8)YES X 2 –  (X+4)(X-4) 9)NO -(4 + 16X 2 )  -(16X 2 + 4) 10)YES √X 4 = X  (X 2 +2)(X 2 -2)

Factoring Method #3 Factoring a perfect square trinomial in the form:

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

Does the middle term fit the pattern, 2ab? Yes, the factors are (a + b) 2 : b a

Does the middle term fit the pattern, 2ab? Yes, the factors are (a - b) 2 : b a

T.O.O: IS IT A PERFECT SQUARE TRINOMIAL? 1)X 2 + 8X )X 2 + 6X – 9 3)X 2 + 5X )X X )4X 2 – 20X )X 2 + 8X )49 – 14Y + Y 2 8)2X 2 + 8X )X 2 – 2X – 3 10)X 2 – 2X + 1

HOMEWORK FACTORING WS #1 FACTORING WS #1