# Unit 2 Quadratic Functions and Factoring Janelle Arquiza
Get Started. It's Free Unit 2 Quadratic Functions and Factoring ## 5. Patterns in factoring

### 5.3. Sum of cubes Ex: x^3+125 (a+b)(a^2- ab+b^2) Same Opposite Always Positive!

5.3.1. Ex: x^3+4^3 (x+4)(x^2- 4x+16) Check work: x^3- 4x^2+16x+4x^2- 16x+64=x^3+64

### 5.4. Difference of cubes Ex: x^3- 125 (a- b)(a^2+ab+b^2) Same Opposite Always Positive!

5.4.1. Ex: x^3- 3^3 (x- 3)(x^2+3x+9) Check work: x^3+3x^2+9x- 3x^2- 9x- 27=x^3- 27

## 6. Factoring trinomials

### 6.1. With leading coefficient= 1

6.1.1. Ex: x^2- 3x- 28 - 7×4=- 28 - 7+4=- 3 (x- 7)(x+4)

### 6.2. With leading coefficient = not 1

6.2.1. Ex: 6x^2- 11x- 2 x^2- 11x- 12 (6x^2- 12x)+(x- 2) 6x (x- 2)+1 (x- 2) (6x+1)(x- 2)

### 7.1. With leading coefficient= 1

7.1.1. 1) Variables on the left, constants on the right. 2) Take 1/2 of the coefficient of the "x" variable term. 3) Square that value and add to both sides of the equation. 4) This makes the left side a Perfect Square Binomial.

7.1.1.1. Ex: x^2+8x- 43=0 x^2+8x=- 43 8/2=4 x^2+8x+16=43+16 x^2+8x+16=59 (x+4)^2=59

### 7.2. With leading coefficient= not 1

7.2.1. 1) Variables on the left, constants on the right. 2) Make leading coefficient =1 by dividing every term by the leading coefficient. 3) Take 1/2 of the coefficient of the "x" variable term. 4) Square that value and add to both sides of the equation. 5) This makes the left side a Perfect Square Binomial.

7.2.1.1. Ex: 3x^2- 6x=31 x^2- 2x=31/3 - 2/2=- 1 x^2- 2x+1=31/3+3/3 (x- 1)^2=34/3

## 8. Discriminants

### 8.3. D=0 1 x- intercept 1 solution

8.3.1. D<0 no x- intercepts 2 solutions