July 15th Class Notes

Algebra: Monomials

What is a monomial?

The points below make a monomial 

Example:

3x²

- The 3 is the number coefficient

- The X is the letter variable

- The 2 is the exponent. If it is a negative or fraction then it is not a monomial

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Degree of a monomial

The sum of all exponents is the degree of a monomial

Example:

3x² has a degree of 2

3x²y⁵ has a degree of 7

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Multiplication of monomials

http://www.mathwarehouse.com/algebra/polynomial/monomials/how-to-multiply-monomials.php

Multiplying monomials will always result in a single term

Multiplying numbers, and add exponents of same variable

Examples:

10ab * 4ab = 40ab²

3x⁴ * 7xy = 21x⁵y

9a³b²c⁵ * 2ab²c⁷ = 19a⁴b⁴c¹²

10 * (2x⁹) = 20x⁹

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Adding and subtracting of monomials

You can only add or subtract coefficients if their variables are exactly the same

Examples:

6x³ + 9x³ = 15x³

4x² + 9x = 4x² + 9x

3(2x²) + 4x(5x) – 2(6x)² = 6x² + 20x² – 72x² = 46x²

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Division of monomials

You can divide coefficients, and subtract exponents of same variables

Examples

10x² / 5x = 2x

24x³ / 6 = 4x³

16x⁶ / 4x⁶ = 4 

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Algebra: Polynomials

What is a polynomial?

A series of more than 3 monomials linked together by a + or –

Binomials are at least 2 monomials linked together by a + or –

Trinomials are 3 monomials linked together by a + or –

Examples:

Binomial – 5x² + 4x²

Trinomial - 5x² - 4x² + 9x

Polynomial - 5x² - 4x² + 9x + 7x

Degree of a Polynomial

The degree of the highest monomial

Examples:

5x² - 4x² + 9x + 7x – has a degree of 2

5x³y⁹ + 4x² + 9x + 7x – has a degree of 11

Algebra: Orders of Operation – BEDMAS/PEDMAS

1.     Brackets/ Parentheses

2.     Exponents

3.     Division

4.     Multiplication

5.     Addition

6.     Subtraction

Algebra: Substitution

When you are given an algebraic expression and told to substitute and solve it.

Use BEDMAS/PEDMAS

Example:

-5x² + 20x + 25         If x = 3

= -5(3)² + 20(3) + 25

= -45 + 60 + 25

= 40

 Algebra: Polynomial Addition and Subtraction

For addition collect like terms

For subtraction multiply negative to second bracket then collect terms

Examples:

(3x² – 2x + 5) + (5x² + 3x – 4)

= 3x² + 5x² – 2x + 3x + 5 - 4

= 8x² + 1x + 1

(2x² + 5x + 8) – (x² – 4x + 5)

= 2x² + 5x + 8 – x² + 4x – 5

= 2x²  - x² + 5x +4x + 8 – 5

= x² + 9x + 3

  

Useful websites

http://www.onlinemathlearning.com/expression-exponent.html