WHRHS 2012-2013 Unit 3 – Polynomials Algebra 2CP Unit 3 Day A ~ Polynomials Monomial - a Number, a Variable or a PRODUCT of a number and a variable. *monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree of a monomial - is the SUM of the exponents of the variable(s) in the monomial. The degree of a constant term is 0. Polynomials – a variable expression whose terms are Monomials. Monomials have 1 term. Binomials have 2 terms. Trinomials have 3 terms. Polynomials with more than 3 terms do not have special names. Polynomials in one variable are usually arranged in descending order so that the exponents of the variables decrease from left to right. *polynomials(just like monomials) cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree of Polynomial – is the Greatest of the degrees of any of its terms. (Remember each term is a monomial so the degree will be the sum of the exponents in the monomial.) Constant Term of Polynomial – Term that does not have a variable attached to it. Leading Coefficient of Polynomial – is the coefficient of the variable with the largest exponent. What Can You Do With Polynomials? Evaluate Polynomials – Just substitute in the assigned value for the variable and find the value of the polynomial. Example: 3x 2 4 x 6 evaluate x = 3. The value of the polynomial will be 45. 3(3)2 + 4(3) + 6 = 45. Add Polynomials – To add polynomials just Combine like terms. There are 2 formats you can use to add polynomials – horizontal format or vertical format. Example: Horizontal Format:( 3x 2 4 x 6 ) + ( 7 x 2 2 x 2 ) = 10x2 + 6x + 4 Vertical Format 3x 2 4 x 6 + 7 x2 2 x 2 10x2 + 6x + 4 Subtract Polynomials – To subtract polynomials just Add the additive inverse of the 2nd polynomial. There are 2 formats you can use to subtract polynomials – horizontal format or vertical format. Example: Horizontal Format :( 3x 2 4 x 6 ) - ( 7 x 2 2 x 2 ) = - 4x2 + 2x + 8 Vertical Format 3x 2 4 x 6 7 x 2 2 x 2 - 4x2 + 2x + 8 WHRHS 2012-2013 Unit 3 – Polynomials Algebra 2CP Part 1: Find the degree of the polynomial. 1. 3x 2 2. 4 x 3 17 x 5 3. 13x n 5 x n 2 4. 0.55 x 2 0.7 x 5. 7 x3 10 x 15 Part 2: Standard form of a polynomial is when the terms are written so that the exponents on the variables decrease from left to right. Write the polynomial in standard form. 6. 3x 2 x 3x3 12 7. 4 x3 3 x 2 8. 4 x 5 2 x 2 9. 7 6 x 3x 2 x 3 Like terms in a polynomial have the same _____________ and the same ___________. Part 3: Identify the like terms and simplify the expression. 10. x 2 5 x3 2 x 3x 2 7 4 x 7 11. 6 x 2 x 12. 2 x 2 13. 15 x 2 5 x2 5 x3 x 2 18 5 x 3x3 8 4 x3 6 x 15 x 7 2 x Part 4: Leading Coefficient and Constant Term. Identify the leading coefficient in each of the polynomials in part 3. 10. _____ 11. _____ 12. _____ 13. _____ Identify the constant term in each of the polynomials in part 3. 10. _____ 11. _____ 12. _____ 13. _____ WHRHS 2012-2013 Unit 3 – Polynomials Algebra 2CP Adding and Subtracting Polynomials To add polynomials – simply combine like terms!! Horizontal Format: 1. (3x2 + 2x - 7) + (7x3 – 3 + 4x2) = 2. (4x2 + 5x – 3) + (7x3 – 7x + 1) = Vertical Format: 3. (2x – 3x2 + 4x3 + 1) + (3x2 – 2x + 7) 4. (5x4 – 2x + x2 + 4) + (-5 + 6x) To subtract polynomials – distribute the negative and then add!! (*Think – subtraction means add the opposite*) Horizontal Format: 5. (3x2 – 7xy + y2) – (-4x2 + 7xy – 3y2) 6. (6x3 – 3x + 7) – (3x2 – 5x + 12) Vertical Format: 6. (3x2 – 2x + 5) – (2 – 3x + 4x3) 7. (5x2 + 3x – 1) – (2x2 + 4x – 6) WHRHS 2012-2013 Unit 3 – Polynomials Algebra 2CP Unit 3 ~ Day A HW Complete the chart below by first rewriting each polynomial in standard form. Then identify the degree, leading coefficient, and constant for each polynomial. Leading Polynomial Rewrite in Standard Form Degree Constant Coefficient 1. -2 + 5x 2. 12 3. -1 – 4x2 + 7x 4. 5x3 – 2 5. 4 – 3x4 6. x2 + 5x + 2x4 – x+1 7. 3x3 – 10x + 15 + 6x5 8. 7x – x5 + 3x2 +3x5 9. 6 – 3x3 10. 5x + 14x4 – 8 – 4x + 2x2 WHRHS 2012-2013 Check the box(es) that describes each polynomial below. Monomial Binomial Unit 3 – Polynomials Algebra 2CP Trinomial 11. x2 – 5x + 7 12. 10x4 13. 3 – 15x3 14. 10x5 – 12x3 + 8 15. 6x9 – 10x5 + 2x – 19 Add or subtract each polynomial. Choose a method (horizontal/vertical): 16. (4x2 + 3x – 5) + (x2 – 7x + 10) 17. (x2 – 2x + 7) – (3x2 – 4x + 7) 18. (4a2 – 7a) – (-6a2 + 5a – 7) 19. (5x2 – 3x + 8) – (x2 – 8x + 12) 20. (3x2 - 2x + 7) + (-3x2 + 2x – 12) 21. (5x2 – x + 6) + (-3x2 + 2x – 12) + (-6x2 + 5x – 7) Polynomial