1. Polynomials
Algebra at its best!

2. Part one Check this out:
Magicians and illusionists use number tricks all the time to try and fool you into thinking that they “magically” arrived at the right answer.
The reality is that algebra helps to solve these number tricks and games.
Every number trick can be explained by using algebraic expressions.
That’s right – number tricks can be solved with math!
(and you say that Math isn’t fun – HAH! )

3. Say what? Math can be fun? Try this trick: What happens???
Ask a person with a two digit age to multiply the tens digit in their age by 5
Then, add 3
Then, double that sum
Next, have the person add the value of the ones digit in their age to their answer from step three
Finally, subtract 6
What happens???
Can you figure out the formula???? (teeheehee )

4. The language of Algebra
Algebra is all about using symbols to represent unknown quantities or amounts
An algebraic expression is basically a mathematics statement that contains some unknown quantities
An algebraic expression can have different parts:
Variables
Coefficients
Constant values
Terms

5. The language of Algebra
Variable
An unknown quantity represented by a letter
Coefficient
A number that multiplies the variable
Constant
A known value in an equation or expression
constant
coefficient
variable
Practice: page 187: #5,6,7

6. The language of Algebra
Algebraic expressions can have a different number of terms
A term is an expression formed from the product of numbers and/or variables, or formed by a constant
examples:
Algebraic expressions can have more than 1 term

7. The language of Algebra
Polynomials are algebraic expressions that are made up of terms connected by addition or subtraction
A monomial has only 1 term
A binomial has two terms
A trinomial has three terms
When there are more then 3 terms, we just use the name polynomial.
Practice: Page 179 #5, 6, 7

8. Part 2 The language of Algebra
Terms and polynomials have degrees
The degree of a term is determined by the sum of the exponents on the variables in a single term
For example: 3xy has a degree of 2
5x²z has a degree of 3
-2b³c has a degree of 4

9. The language of Algebra
The degree of a polynomial is the degree of the highest degree term in the polynomial
For example:
This polynomial has a degree of 5
(the first term has a degree of 5,
the second term has a degree of 2.
The highest degree is 5, so the degree of the polynomial is 5
Practice: page 179: #8, 9, 10

10. Time to practice applying this!
Page 180 #19, 21, 23, 24, 26, 29
Worksheet: turning words into algebraic expressions

11. Part 3 The language of Algebra
The standard form for writing polynomials with many terms, some of which have the same variable, is with the highest degree term first
Non-standard form example: 3x x3 + x6
BUT…this is the correct, standard form:
The highest degree is 6, so that goes first, then 3, 2 and then the constant last:
x6 + 4x3 + 3x2 - 7

12. The language of Algebra
Algebraic expressions can contain like terms. So, what is a like term??
Basically, like terms have the same variable and differ only by their coefficients!
Like terms:
-7x and 3x w², 3w², and -0.5w²
Examples that are NOT like terms:
6x and 3x³ m²n and 4mn²
Like terms can be combined!!
Practice: page 187 #8,9,10,11,12

13. Time to practice applying this!
Page 188: #15, 16, 17, 18, 19, 20, 21, 22
Page 182 – Math Link