Degrees In Polynomials(:

Degree 0 - Constant

Degree 1 - Linear


Degree 2 - Quadratic


Degree 3 - Cubic


Degree 4 - Quartic

Degree 5 - Quintic

Degree 6 - The Sixth Degree

Identifying Special Situations In Factoring (:

• Difference of two squares
  • a²- b² = (a + b)(a - b)
    • (2x+1)(2x-1)
    • (3x-2)(3x+2)
    • (x-10)(x+10)
• Trinomial perfect squares
• a² + 2ab + b²= (a + b)(a + b) or (a + b)²
• x²-x+4 = (x-2)²
• x²+6x+9 = (x+3)²
• x²+10x+25 = (x+5)²
• a² + 2ab + b²= (a + b)(a + b) or (a + b)²
• 16x² - 8xy + y² = (4x - y)²
• ^{8xy + y2 + 16x2 = 16x2 + 8xy + y2 = (4x + y)2}
• Difference of two cubes
  • a³ - b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • x³-27 = (x-3)(x²+3x+9)
      • s³-1 = (s-1)(s²+s+1)
      • 8y³-125 = (2y-5)(2y²+10y+25)
• Sum of two cubes
  • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • z³+1 = (z+1)(z²+z+1)
      • x³+64 = (x+4)(x²-4x+16)
      • y³+125 = (y+5)(y²-5y+25)
• Binomial expansion
• (a + b)³ = x³ + 3x²y + 3xy² + y³
• (a + b)⁴ = (x+y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴

Domain X Values & Range Y Values (End Behaviors)

∞ = Infinity(:

domain → +∞, range → +∞ *rises on the right*
domain → -∞, range → -∞ *falls on the left*

domain → -∞, range → +∞ *rises on the left*
domain → +∞, range → -∞ *falls on the right*

domain → +∞, range → +∞ *rises on the right*
domain → -∞, range → -∞ *falls on the left*

domain → +∞, range → -∞ *falls on the right*
domain → -∞, range → -∞ *falls on the left*

Scalar Multiplication / Multiplying Matrices (:

Scalar Multiplication

[ 2   3   5  ] + [ 7  5  9  ] = [ 9  8  14  ]

> Scalar Multiplication is the process of taking the outside number of

matrices and distributing that number to ALL the numbers in the bracket.

.. As shown above.

Multiplying Matrices

In multiplying matrices, the first thing to observe is rows and columns.

The rows and columns of a matrix can tell you whether or not the matrix

can be multiplied. A dimension statement shows that the columns of the first

matrix match up to the rows of the second matrix.

2 X 2 times 2 X 2

- the 2's being the same on the inside indicate that the matrix CAN be multiplied.

Multiplying The Matrix . . .

Procedure: Multiply the first number in the first row by the first number in the

first column of the second matrix. Add the products together and repeat this

procedure until you have multiplied all the numbers in the matrices, thus giving

you the product of your matrices.

Determine If A Quadratic Equation Is A Circle, Parabola, Hyperbola or Ellipse (:

4x² +4y² =36

Terms A & C [4] are the same, therefore
making the equation a circle.

The Rule - "If A=C, then the equation is a Circle.

2x² + 4y=3

Equation that is missing X or Y² is a Parabola
 4x² - 4y² = 12

If A or C are different signs, the equation is a Hyperbola

4x² + 3y² = 25

If A does not equal C, and they are the same sign, then the equation is a Ellipse

Dimensions of a Matrix

The Number of columns in A must be equal to the number of rows in B to be multiplied. 

1 X 3

3 X 3

3 X 3

2 X 3

Error Analysis (:

The inputs increase by 5. The output values represent the table 2x+9

(1,2) is the solution of the 5x-7 but not a solution to x+4y

For problem 22, The inequality should be a dotted line because it's less than without an equal sign. For problem 23, the shading should be above the line as compared to the picture which is shaded below.

For these set of inequalities, the shading is correct but the lines have to be dotted instead of straight. The line should be straight because the sign is less than/greater than or equal to.