Identifying Special Situations in Factoring

Difference of two squares

-a²- b² = (a + b)(a - b)

Trinomial perfect squares

--a² + 2ab + b²= (a + b)(a + b) or (a + b)²

^{--a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}

Difference of two cubes

--a³ - b³

3 - cube root 'em

2 - square 'em

1 - multiply and change

Sum of two cubes

--a³ + b³ 

3 - cube root 'em

2 - square 'em

1 - multiply and change

Binomial expansion

--(a + b)³ 

--(a + b)⁴

 

Naming Polynomials and End Behaviors

Linear Equations:
y=mx+b (1 degree, 0 turns)
m: slope
b: y-intercept

Domain= x-values
Range= y-values

When m is positive: falls to the left, rises to the right

domain → +∞, range → +∞

domain → -∞, range → -∞

When m is negative: rises to the left, falls to the right

domain → -∞, range → +∞

domain → +∞, range → -∞

Quadratic Equations:
 --Parabolic Equations
y=ax² (2 degree, 1 turn)

(a+b)(c+d)

When a is positive: rises to the left, rises to the right

domain → +∞, range → +∞ (rises on the right)

domain → -∞, range → -∞ (falls on the left)

When a is negative: falls to the left, falls to the right

domain → +∞, range → -∞ 

domain → -∞, range → -∞

***Number of turns is always one less than the degree!

Degree:

0- Constant 

1- Linear

2- Quadratic 

3- Cubic

4- Quartic

5- Quintic 

6 to ∞- nth Degree 

Terms:

Monomial 

Binomial 

Trinomial 

Quadrinomial 

Polynomial

Identifying Quadratic Equations

STANDARD FORM: ax² + bx + cy² + dy + e= 0 

If a is not equal to c and the signs are the same then the equation is an ellipse:

If a or c have different signs then the equation is a hyberbola:

If a or c=0, then the equation is a parabola:

If a=c, then the equation is a circle: