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Factoring Polynomials. Factoring: Factoring: Quadratic Trinomials into 2 Linear Binomials Using Tiles: 1)What polynomial is represented below? 2)Convert.

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Presentation on theme: "Factoring Polynomials. Factoring: Factoring: Quadratic Trinomials into 2 Linear Binomials Using Tiles: 1)What polynomial is represented below? 2)Convert."— Presentation transcript:

1 Factoring Polynomials

2 Factoring: Factoring: Quadratic Trinomials into 2 Linear Binomials Using Tiles: 1)What polynomial is represented below? 2)Convert the mass of tiles into a single rectangle. 3)The dimensions of the rectangle are the factors!

3 Factoring: Factoring: Quadratic Trinomials into 2 Linear Binomials Remember that the x 2 tiles have to be in the top left corner and the unit tiles have to form a rectangle in the lower right corner. The x tiles fill in the spaces.

4 Factoring: Factoring: Quadratic Trinomials into 2 Linear Binomials If you want to factor without the tiles, you have to guess and check. Heres an organized way to do just that. 1)Find the factors of the c term. 2)The factors that add up to the b term are the correct ones. 3)Check the signs to make sure they will multiply correctly! 4)Check your answer!

5 Factoring: Factoring: Quadratic Trinomials into 2 Linear Binomials Try these examples: 1)x 2 + 7x + 122) x 2 + 8x + 12 3) x 2 + 2x – 34) x 2 – 6x + 8 5) x 2 + x – 126) x 2 – 3x – 10 7)X 2 – 8x + 158) x 2 – 3x – 18 9) x 2 – 3x + 210) x 2 – 10x + 21

6 Factoring Special Cases: Perfect Square Trinomials A trinomial formed by squaring a binomial. Ex1: (x + 5) 2 Ex2: (2x – 3) 2 Ex3: (x - 4) 2 Ex4: (5x + 2) 2 What do you notice about the resulting trinomials?

7 Factoring Special Cases: Perfect Square Trinomials Perfect Square Trinomial (a +b) 2 = a 2 + 2ab + b 2 (a – b) 2 = a 2 - 2ab + b 2

8 Factoring Special Cases: Perfect Square Trinomials Determine whether the following polynomials are perfect square trinomials. If so, factor it. 1)x 2 – 12x + 36 2)9x 2 + 34x + 25 3)x 2 + 18x + 81 4)64x 2 - 20x + 1

9 Factoring Special Cases: Difference of Squares A binomial that is created by subtracting two perfect squares. Ex1: x 2 – 4Ex2: x 2 – 625 Ex3: 4x 2 – 25Ex4: 16x 2 - 81 What is true about the factored form of each of these binomials?

10 Factoring Special Cases: Difference of Squares Difference of Squares a 2 – b 2 = (a + b)(a - b)

11 Factoring Special Cases: Difference of Squares Factor each of the following completely: 1)x 2 – 100 2)x 4 – 16 3)100x 2 – 400 4)3x 2 - 75 5)225x 2 – 121y 2 #2 isnt quadratic and #5 isnt a polynomial, but you can still factor them!


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