This is a PowerPoint on teaching the subject of Polynomials, Monomials, and Rational Expressions, dealing with how to add, subtract, multiply, and simplify all of these.

1. Adding, Subtracting, Multipl
ying, and Simplifying

2. Monomials
 An algebraic expression consisting of
one term.
 Examples of a monomial :
 5x^2
 9ab
 Not a Monomial :
 2x+7
 4x^2+3x-9

3. Polynomials
 An expression of more than two
algebraic terms.
 What makes terms not polynomials?
 Cannot have a negative exponent.
 Cannot have variables in the
denominator.
 Cannot have variable inside a radical.

4. Polynomial or not?
 1/x^2-12x+1
 No
 Square Root of x+3x-8
 No
 6x^(-3)-3x+7
 No
 3x^2+2x-4
 YES

5. Rational Expressions
 Any expression that can be written as the
ratio of two polynomial expressions.
 Cannot have a denominator with :
 Zero
 Square Root
 Examples of Rational Expressions :
 1/(x-1)
 Xy^2-y

6. Rational Expression or Not?
 6x/(x-1)
 YES
 3x-2/0
 No
 3/14x-5
 YES
 4x/Square Root of 7
 No

7. Adding Polynomials and
Rational Expressions
 Only add if you have like terms
 If you do, Add together like terms
 Example :
 (2x^2-3x+4) + (8x^2-4x-16) =
 10x^2-7x-12
 Try This One :
 (X^2+6x-17)+(3x^2-9x+11) =

8. Subtracting Polynomials and
Rational Expressions
 Only subtract if you have like terms
 If you do, subtract like terms
 Example :
 (6x^2+12x+8) – (4x^2+9x+9) =
 2x^2+3x-1
 Try this one :
 (3x^2-4x+19) – (2x^2-8x+18) =

9. Examples for you to Try
 Addition :
 (18x^3+x^2+3x-1) + (2x^3-3x^2+8x+3)
 (8x^3+7x-9) + (9x^2-8+6x)
 Subtraction :
 (7x^2-2x-90) – (28x^3+20x-90)
 (8x^2-7x+3) – (18x^4+44x-18)

10. Cross Multiplying and Factoring
 Dealing with multiplication and division
 Cross out and cancel like terms
 Example : 4x/8 = x/2
 Take 4 out of top and bottom
 Do this until you cannot factor anymore

11. Multiplying Polynomials
 If there is no denominator :
 Multiply Like terms
 Powers on terms are to be added
 If there is a denominator :
 look to cancel like terms
 Look to Cancel x terms/variables
 Look to factor common factors (Ex. 4/8 or
3/6)

12. Examples of Factoring and
Cross Multiplying
 (8x/3)*(9x/4)
 (8*x/3)*(9*x/4)
 6x^2
 (4x^2/10x)*(5x^2/8x^2)
 (4*x*x/10*x)*(5*x*x/8*x*x)
 x/4
 Try this one :
 (9x^2/26x)*(13/81x) =

13. Examples of Multiplying
Polynomials
 (5x^2)*(-2x^3) =
 -10x^5
 (x^2-4)/(x-3)*(x^2-9)/(x+2) =
 (x-2)*(x+3)
 Try these :
 (3x^2)*(4x^4) =
 (x+4)/(x^2-36)*(x-6)/(x^2-16) =

14. Non-Factorable Multiplication
Problems
 Multiplication where factoring will not
work
 This means it is absolutely simplified
 Check Work always to make sure
 Example :
 (x-2)/(7)*(3)/(x) =
 3(x-2)/7x

15. Tips to Remember
 Always check your work!
 Always look to simplify when possible
 Do not skip steps
 That is where most mistakes occur
 Take your time

16. Credits
Dictionary.com