Ms. K: Algebra 2 Factoring Review

Definitions

100

What is standard form of a quadratic function?

y = ax² + bx + c, where a is not 0.

200

What is the vertex form of a quadratic function?

y = a(x - h)² + k

300

What is intercept form of a quadratic function?

y = a(x - p)(x - q)

400

What is a y-intercept of the function:

f(x) = -2x² + 8x -11

y-intercept (x=0): y = -11

500

What are the coordinates of the vertex of the following quadratic function:

g(x) = 2x²  - 12x + 20 

What is a V(3, 2)?

Special Formulas

100

25x² - 9y²

What is (5x-3y)(5x+3y).

200

x² - 12x + 36

What is (x-6)²

300

49a⁴ - x⁶

What is (7a²-x³)(7a²+x³).

400

81b² - 100c²d²

What is (9b-10cd)(9b+10cd)

500

x⁴ - y⁴

What is 

(x² - y²)(x² + y²) =

= (x - y)(x + y)(x² + y²)

GCF

100

3x² + 6x

What is 3x(x + 2) ?

200

5x³ - 35x

5x(x² - 7)

300

4x³ + 6x + 2x²

2x(2x² + 3 + x)

400

6x²y³ + 9xy²

What is 3xy²(2xy + 3)

500

Factor completely:

6x³ - 24x

What is   6x(x² - 4) =

= 6x(x - 2)(x + 2)

Grouping

100

2x² + 10x + 5 + x

(2x + 1)(x + 5)

200

x³ - 4x² -5x + 20 

(x-4)(x² -5) 

300

20x³-25x²+4x-5

 (5x²+1)(4x-5) 

400

x³+7x²-2x-14

 (x²-2)(x+7) 

500

Factor completely:

x³ - 4x² -4x + 16

 (x-4)(x² -4) = (x - 4)(x - 2)(x + 2)

"ac and b" Method

100

x² + 6x +8

 (x + 2)(x + 4)

200

x² - x - 6

 (x − 3)(x + 2)

300

x² + x - 30

 (x + 6)(x - 5)

400

2x² + 15x + 28

(2x + 7)(x + 4) 

500

Factor :

6y² - 7y - 5

(3y - 5)(2y + 1)