Adding, Subtracting,Multiplying, and Simplifying
Monomials An algebraic expression consisting of  one term. Examples of a monomial :   5x^2   9ab Not a Monomial :   ...
Polynomials An expression of more than two  algebraic terms. What makes terms not polynomials?   Cannot have a negative...
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
Rational Expressions Any expression that can be written as the  ratio of two polynomial expressions. Cannot have a denom...
Rational Expression or Not?   6x/(x-1)     YES   3x-2/0     No   3/14x-5     YES   4x/Square Root of 7     No
Adding Polynomials and       Rational Expressions Only add if you have like terms If you do, Add together like terms Ex...
Subtracting Polynomials and        Rational Expressions Only subtract if you have like terms If you do, subtract like te...
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)   Subtracti...
Cross Multiplying and Factoring Dealing with multiplication and division Cross out and cancel like terms     Example : ...
Multiplying Polynomials   If there is no denominator :     Multiply Like terms     Powers on terms are to be added   I...
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...
Examples of Multiplying           Polynomials   (5x^2)*(-2x^3) =     -10x^5   (x^2-4)/(x-3)*(x^2-9)/(x+2) =     (x-2)*...
Non-Factorable Multiplication             Problems Multiplication where factoring will not  work This means it is absolu...
Tips to Remember Always check your work! Always look to simplify when possible Do not skip steps     That is where mos...
CreditsDictionary.com
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Power Point Part 1

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Transcript of "Power Point Part 1"

  1. 1. Adding, Subtracting,Multiplying, and Simplifying
  2. 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. 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. 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. 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. 6. Rational Expression or Not? 6x/(x-1)  YES 3x-2/0  No 3/14x-5  YES 4x/Square Root of 7  No
  7. 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. 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. 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. 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. 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. 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. 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. 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. 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. 16. CreditsDictionary.com
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