Polynomials
What is a constant?
A number without a variable.
Solve: 3 - 4 + 8 * 2
15
Expand this expression: (x - 3) (x + 4)
x2 + x - 12
(x - 1) (x + 1)
What is a coefficient?
A number that multiples a variable.
Solve: 3 * 4 + 2 / 1 - 10
4
Expand this expression: 3(3x - 2)
9x - 6
Factor: x2 - 7x
x(x - 7)
What is a polynomial?
An expression with variables and exponents.
What does PEMDAS mean?
P- Parentheses
E- Exponents
M- Multiplication & D- Division
A- Addition & S- Subtraction
Expand this expression: (2x - 7)2
4x2 - 14x + 49
Factor: x2 + 5x - 14
(x + 7)(x - 2)
What is the degree of a polynomial?
The highest exponent from the expression.
What are the rational numbers?
Zero and all negative or positive numbers, including fractions and repeating decimals.
Expand this expression: 5x(2x -3)
10x2 + 15x
Factor: x3 + 3x2 -10x
x(x - 2)(x + 5)
What does 3x2 - 11 + 6 factor to?
Yes, (3x - 2)(x - 3)
Is pi a rational number? Why?
No, because the decimal does not stop or repeat.
Expand this expression: 3x(x - 2)(x + 2)
3x3 - 12x
Steps-
Foil: (x - 2)(x + 2) = x2 + 2x - 2x + 4
Add like terms: 2x - 2x = 0
Distrubte: 3x(x2 + 4) = 3x3 - 12x
Factor: 4x2 - 12x + 9
(2x - 3)2