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9.1 Add and Subtract Polynomials Name ____________________ VERY IMPORTANT VOCABULARY!!!!! STANDARD FORM: terms are placed in largest degree to _____order, from the degree (largest exponent, to smallest exponent) DEGREE: largest degree of the polynomials terms (look at the exponents!) LEADING COEFFICIENT: polynomial in standard form, the ___ of the _________ term EXAMPLE: -4x2 + x3 + 3 - 5x4 Individual Terms: -4x2 , x3 , 3, -5x4 Standard Form: -5x4 + x3 – 4x2 +3 Degree: 4 Leading Coefficient: -5 Classification of Polynomials by number of terms Classification Definition Example Monomial Polynomial with only _____ term 6 -2x Binomial Polynomial with _____ terms 3x + 1 4x3 – 5x Trinomial Polynomial with _______ terms 2x4 – 3x2 + 4 Practice: 1) Write the polynomial in standard form 2) find the degree 3)classify the polynomial by the number of terms Standard Form Degree Name 2 3 1. 9x + 8x – 4x + 3 2. 5x + 6 – 3x3 3. –3x – 4x2 4. 5x3 Chapter 9 starts off with adding polynomials. You already know how to do this! Circle the like terms: 5x How do we add like terms? 2y 9x 3x2 5x + 2y + 9x + 3x2 = Now, simplify each expression by combining like terms. Remember, DON’T CHANGE THE EXPONENTS! 1. 8x 2y 3x 2. 3x 7x 3. 6x 2 4x 3x 2 4. x 2 9 6x 2 5. 6x2 3x 2x 2 6. 4x 2 3x 7 x 2 8x -------------------------------------------------------------------------------------------------- Polynomial Addition: Example: (3x2 + 2x − 6) + (5x2 − 8x + 5) Combine like terms: You can also use Vertical Format: 3x2 + 2x − 6 +(5x2 − 8x + 5) Practice: 1. ( 5x3 – x + 2x2 + 7) + ( 3x2 + 7 – 4x) + (4x2 – 8 – x2) 2. ( 2x2 + x – 5) + ( x + x2 + 6) Polynomial Subtraction: Change the – to a + and switch the signs of the terms in the second polynomial think of it as _______________________________ Example: (3x2 + 2x − 6) - (5x2 − 8x + 5) Switch from subtraction to addition and combine like terms: Vertical Format: Practice: 1. ( -2x3 + 5x2 – x + 8) – ( -2x3 + 3x – 4) 2. (x2 – 8) – ( 7x + 4x2) 3. (3x2 – 5x + 3) – (2x2 – x – 4) 4. (5x2 3x 9) (2x2 4x 2) 5. ( x2 3) ( 4x 2 7 ) Mixed Practice: 6. 7. 8. (x2 7x 2) (x2 5x 1) (3x 2 5x 1) (4x 2 7x 2) (2 x3 7 x 2 2) ( x 2 5 x 1) 9. (7x3 7x2 8) (2x2 1) (6x2 5x 2) 10. Find the perimeter: 3 x- 5 4x - 6 2 x +4 Chapter 9 Vocabulary Equation Expression Term 5x – 6 = 3x + 2 Mathematical sentence formed by placing the symbol = between two expressions Variable 2x – 3 or 5x Combination of variables, #’s, and operations x2 – 5x + 6 ( 3 terms) The parts of the expression that are added together Exponent Base x, y , a Letter used to represent one or more numbers 34 34 Coefficient Monomial Degree of a Monomial 3x – 6 3x, 10, ½ ab2 Number part of a term with a variable part A number, a variable, or the product of a number and one or more variables with whole number exponents The sum of the exponents of the variables in the monomials Polynomial Degree of a Polynomial Binomial 2x3 + x2 – 5x + 12 Is a monomial or a sum of monomials 2x3 + x2 – 5x + 12 Degree: 3 The greatest degree of its terms 6n4 – 5n2 Trinomial Descending Order or Standard Form Not in standard form 15x – x3 + 3 Leading Coefficient 2x2 – x – 4 Polynomial with three terms Standard form: -x3 + 15x + 3 Polynomial with two terms 2x3 + x2 – 5x + 12 Coefficient of the first term Example of a 2nd degree Binomial Example of a 3rd degree Trinomial Example of a 4th degree monomial x2 – 5x a3 – a2 + 8 5x4