1. Adding, Subtracting,
Multiplying, 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