Welcome!Mrs. GillenMath 2

Last Night’s Homework: Unit 2.1 HWTonight’s Homework: Unit 2.2 HW

Quiz: Tuesday 9/18

Warm upFactor out the greatest common factor(GCF):

1) −2𝑥3 − 16𝑥 2) 45x + 3y

Simplify: Solve:

3) 124 4) -24

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Pg. 109

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Pg. 110-111

Pg. 111

Pg. 111

Unit 2.2 Factoring Special Products

Factoring (Review)The process of breaking a polynomials down into smaller parts, that are called factors. This can be thought of as reversing multiplication.

𝒙𝟐 − 𝟐𝟓 = (𝒙 + 𝟓) ∙ (𝒙 − 𝟓)

Factors

Factoring Differences of Two Squares

Difference of Two squares = Sum ● Difference

(a + b)(a – b)a2 – b2 =

Factoring 𝒂𝟐 − 𝒃𝟐 always results in (a+b)(a-b)

Step 1: Write the two parentheses(one with a + sign & one with a - sign)

Step 2: Find 𝒂𝟐 = 𝒂 & 𝒃𝟐 = 𝒃

Step 3: Fill in parentheses / check w/FOIL

9x2 – 16

PracticeCompletely factor the following differences of two squares.

1. 𝒙𝟐 − 𝟑𝟔 2. 𝟖𝒙𝟐 − 𝟓𝟎

3. 𝒙𝟐 + 𝟐𝟓 4. −𝒙𝟐 + 𝟒𝟗

Detecting & Factoring Perfect Squares

x2 - 4x + 4 is a Perfect Square Trinomial

Second TermFirst Term Third Term

x2 = x 𝟒 = 24x = 2(x)(2)a2 b22ab

x2 – 4x + 4 = 𝒙 − 𝟐 𝒙 − 𝟐

𝒂𝟐 ± 𝟐𝒂𝒃 + 𝒃𝟐 = 𝒂 ± 𝒃 𝟐

Factoring a Perfect Square Trinomial

x2 + 12x + 36

4x2 – 20x + 25

HomeworkHW p.112 #20-30

p. 113 #11-22