Polynomials, Exponents and Factoring

To write a number or expression as a product of two or more other numbers or expressions is to:
(Ex:  x² + 2x -3 = (x + 3)(x - 1))

• Verify
• Expand
• Simplify
• Factor

A number (ex: 5), a variable (ex: x), a product of numbers and variables (ex: 3x), or a product of variables (ex: xy) is called a:

• Variable
• Term
• Factor
• Binomial

To use the rules of arithmetic and algebra to rewrite an expression as simply as possible is to:
(Ex: 3x³ + x³ + √4 + 1 =  4x³ + 3)

• Expand
• Verify
• Simplify
• Factor

A number or expression is considered __________ when each of its factors cannot be factored any further.

• Fully Factored
• Expanded
• Verified
• Factored

A value that does not change or a number on its own in an expression is a:
(Ex: 5,  23,  or  8 in: x² + 3x + 8)

• Term
• Binomial
• Constant
• Coefficient

The sum of a number of terms whose variables have whole number exponents is a
(Ex:  8x,   2y³ + y,  3x + 1,  4x² + 5x + 10,  8xy² - 3xy - 5x - 6)

• Polynomial
• Binomial
• Fully Factored
• Degree

The following:
(5/x) + (x^1/2) + 3
(∛x⁵)+ (x/3) + 2 
x^-2 
Are examples of:

• Polynomials
• Binomials
• Algebraic Expressions
• Constants

Substitute a value into an equation by replacing a variable with it and confirm that an equation is true 
Ex:   5x + 2 = 12   let x = 2  
5(2) + 2 = 12
10 + 2 = 12
12 = 12

• Simplify
• Verify
• Expand
• Factor

A polynomial with 2 terms
Ex: (x) + 3,  3 + y,  a² + b²,
 c - 9,  (-x² - 9)

• Trinomial
• Quadratic
• Coefficient
• Binomial

To write the product of factors that are written as polynomials into one longer polynomial is to 
Ex: (x + 2)(-x -1) =  -x² -3x -2

• Expand
• Simplify
• Factor
• Verify