The document provides examples and steps for factoring different types of polynomials: 1) It shows how to factor binomials that are the difference of squares, like x^2 - 9, by finding the roots. 2) It demonstrates factoring a perfect square trinomial by identifying the pattern a^2 + 2ab + b^2 and grouping terms. 3) It presents the formula for factoring the sum or difference of two cubes, like 8x^3 + 27, by treating it as (a)^3 + (b)^3 and grouping the terms.

1. Factoring Polynomials Mr. Trinh Algebra 1 8-9-11

2. Objective: Students identify and factor binomials that are the differences of squares when given examples. Students identify and factor perfect square trinomials when given examples. Students identify and factor difference of two cubes when given examples.

3. Example #1 Factor: x 2 -9 Solve for the roots of x by setting it equal to zero. x 2 -9=0 Solve for x: x=sqrt(9) So x=+3, -3 Therefore, x 2 -9 = (x-3)(x+3)

4. Example #2 Factor: a 2 - (1/9) Step 1: Find the roots by setting the eqn.=0 Step 2: Solve for a. Step 3: Replace the solutions as the roots of x a 2 - (1/9) =0 a2=(1/9) a= +(1/3), -(1/3) [a+(1/3)][a-(1/3)]=0

5. Factoring Perfect Square Trinomials Properties of a trinomial: 1. The square of the first term of the binomial: a² 2. Twice the product of the two terms: 2ab 3. The square of the second term: b² 4. Every perfect square trinomial has the form: a²+2ab+b² Examples: #1: (x+5) 2 = x 2 +10x+25 #2: (a+b)(a+b)=a 2 +2ab+b 2

6. Factoring the sum or difference of two cubes The Formula: Example: 8x 3 + 27 = (2x)3 + (3)3 = (2x + 3) (4x 2 - 6x + 9) Because a=2x, b=3

7. The End