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CC Math I Standards: Unit 6 POLYNOMIALS: INTRODUCTION MONOMIALS: EXAMPLES: 4 A number y A variable NON-EXAMPLES: Variable as an 2x exponent 2 x 3 A sum a2 The product of variables 5 a 2 3 x 1 2 The product of numbers x y and variables 2 Negative exponent A quotient Examples: Determine if each expression is a monomial. 2 1 x 1. 4 xy 2. a 8 4. 7 z 3. 5 7 5. b POLYNOMIAL: A polynomial is a ________________ or the _______________________________________ of different monomials. 6. 2q Determine which expressions are polynomials: a c ab d 7. 8. p + q 9. 10. x2 + 4x – 8 11. 7y3 – 5y -2 + 4y 4 d BINOMIAL: SPECIFIC TYPES OF POLYNOMIALS TRINOMIAL: Examples: Examples: Examples #12 - 19: Determine if each expression is a monomial, binomial, trinomial, or not a polynomial. 12. 2m 7 13. x 2 3 x 4 5 14. 5 3 2x 15. 3 y 2 6 7 y 16. 3x + 8x – 5x2 17. 8x3y2z 18. 2a2 + 3ab – 5ba 19. 9r + 11 – 5r2 CC Math I Standards: Unit 6 POLYNOMIALS: ADDITION AND SUBTRACTION WARM UP ACTIVITY: Simplify the following 1) 3x – 2y + 4y – 6x 3) 4z + 2t + 3z – t 2) 3x – 12y – 2x2 + 6y 5) 8a + 6b + 6a + 2b 4) 5a + 3b – 2c – 8a ADDING AND SUBTRACTING POLYNOMIALS: When adding and subtracting polynomials, you COMBINE LIKE TERMS. Be careful of parentheses and positive or negative signs with the operations. Exp 1: (3x2 – 4x + 8) + (2x – 7x2 – 5) Exp 4: (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2) Exp 2: (3n2 + 13n3 + 5n) – (7n + 4n3) Exp 5: (7y2 + 2y – 3) + (2 – 4y + 5y2) Example 3: (2b2 + 8ab3 + 4b) – (9b – 5ab3) Exp 6: (3x2 + 5x + 2) – (4 – 2x) + (5x2 + 7) PRACTICE PROBLEMS: Simplify each expression 2. ( 3 x 5) ( 2 x 3) 2x 3 2x 2 7x 9 1. x2 3. ( 2 x 3) (4 x 3) 4. (2 x 2 2 x 4) ( x 2 3 x 7) 5. (3a 2 a 4) (a 2 2a 1) 6. ( t 2 1) ( 2t 3) 7. ( 2 x 2 3) ( x 2 2 x 1) 8. (2 x 2 5 xy 3 y 2 ) (8 x 2 7 y 2 ) 9. ( z 2 2z 5) ( 3 z 2 z 4) 10. ( 4m 3n ) ( 2n 5m ) Find the PERIMETER of the shape. Equation: Perimeter = Sum of all the sides 3 – 2x 4x - 8 3a - b 3a - b 11 + y 3a - b 2y – 3x - 3 9x – 3y + 2 12 + 5x + 7y 7 + 3x 3b – 4a + 5 6 + 2a 6 + 2a 4z + 3 5x2 – 2 4z + 3 3b – 4a + 5 Find the sum or difference: 1) (x3 - 7x + 4x2 – 2) – (2x2 – 9x + 4) 2) (3a + 2b – 7c) + (6b – 4a + 9c) Word Problems: 1) Bob mowed (2x2 + 5x – 3) yards on Monday, (4x – 7) yards on Tuesday, and (3x2 + 10) yards on Wednesday. a. How many yards did he mow in the three days? b. If Bob mowed 14x2 + 12x – 3 yards total for the entire week, how many yards did he mow during the rest of the week? 2) Molly has (4x + 10) dollars and Ron has (-5x + 20) dollars. a. How much money do they have altogether? b. How much more money does Molly have than Ron? POLYNOMIALS: Multiplication of Monomial and Polynomial DISTRIBUTIVE PROPERTY REVIEW 1) -4 (2 – 6x ) 2) 3 (5p + q – 3r) 3) -2 (-x - 7y) SIMPLIFYING PRACTICE PROBLEMS: 1) (4x + 7x)3 2) 12z – 5z + 9z2 3) -7 (– 6m + 11m) 4) 4(11 – 3x) 5) – 5(5a – 3b – 6) 6) -2(x2 - 8x + 3x3 – 6) 7) 9x – 4(6 – 3x) 8) 5(3b – 2a) – 7b 9) 12 + 3(7x + 2) 10) 6(4y + 3z) – 11z 11) 5 + 2(4m – 7n) + 9n 12) 12 –7(3 – 5r) + 8r