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Name _______________________ Score _________ Algebra 1B Assignments Chapter 9: Polynomials and Factoring 9-1 Pages 497-499: #1-5, 11-18, 24-27, 31-41, 72-75 9-2 Pages 501-503: #2-12 even, 13-32, 34-37, 52-64 even 9-3/ 9- 4 Pages 507-510: #5-10, 20, 21, 30-39, 65, 68, 73, 74 Pages 515-516: #2-8 even, 15-17, 26, 27, 32, 33, 42, 44, 47 Quiz 9-1 to 9-3 Worksheet: Review of Polynomials 9-5/ 9-7 Pages 521-523: #6-11, 22-27, 36, 37, 75-77 Pages 531: #1-4, 13-15 9-6/ 9-7 Pages 525-526: #2-12 even, 16-19, 25-27, 31, 44 Pages 531: #8, 10, 11, 25-27, 38 Review Worksheet: Chapter 9 Review Test Chapter 9: Polynomials and Factoring Page 548: #1-26 Section 9-1 Warm – Up: Simplify each expression. 1. 2 x 9 7 x 3 2. 6(3 x 4) 3. 7 (2 x 8) 3 4. 5(4 x 1) 2(8 x 6) Objective: To describe polynomials To add and subtract polynomials k polynomial - An expression which is the sum of terms of the form nonnegative integer. ax where k is a Example #1: Which of the following is not a polynomial? 2 12 c 5 x y n 4 a 3 degree of a monomial - The sum of the exponents of its variables. Example #2: What is the degree of each monomial? 4 3 7a 2x y 5 6m n 18 standard form - The degrees of the monomial terms decrease from left to right. leading coefficient - The coefficient of the first term when written in standard form. degree of a polynomial - The largest exponent of its terms. Example #3: Consider the polynomial 7 x 2 5 x 3 4x a) Write the expression in standard form. b) What is the leading coefficient? c) What is the degree of the polynomial? 2 Classifying Polynomials by Degree: Degree Name 0 constant 1 linear 2 quadratic 3 cubic Classifying Polynomials by Number of Terms: # of Terms Name 1 monomial 2 binomial 3 trinomial Example #4: Write each expression in standard form. Then name each polynomial by its degree and number of terms. 3 a) 8x 4x b) 3w 5 w c) 2 2 7 y d) 6 e) 9 3z Example #5: Simplify each sum. a) (8 a 2 3 a 9) (5 a 2 7 a 4) 2 b) (3 x 6 x ) ( 2 x x 2 7) Example #6: Simplify each difference. a) (3c 2 b) ( 6 x 8 c 1) (7 c 3 2 2 c 4) 3 5 x 3) (2 x 4 x 2 3 x 1) Closure Question: What is the difference between adding and subtracting polynomials? Section 9-2 Warm – Up: Simplify each expression. 1. (4 x 2 6 x 7) (2 x 2 9 x 1) 2. (3 x 2 5 x 2) (8 x 2 3. 8(2 y 1) 4. 7(5 2 x ) 10(4 x 3) Find the greatest common factor. 5. 9, 15, 21 6. 12, 20, 28 x 6) Objective: To multiply a polynomial by a monomial To factor a monomial from a polynomial Example #1: Simplify each product. a) 2 g (3 g 2 7 g 5) 2 b) 3 h ( 4 h 3 6h 2 8 h 1) Example #2: Simplify. Write in standard form. a) y ( y 2) 3 y ( y 5) 2 b) a ( a 1) a ( a 2 3) greatest common factor (GCF) - The greatest factor that divides evenly into each term of an expression. Factoring a polynomial reverses the multiplication process. To factor a monomial from a polynomial, find the GCF of its terms. Example #3: Find the GCF of the terms. a) 2 x 4 10 x 2 6x b) 15 c Example #4: Factor each polynomial. a) 16 n b) 9 z 2 2 c) 14 x 12 n 24 15 z 5 21 x 4 7x 2 Closure Question: Explain how to find the GCF of a polynomial. 4 10 c 3 25 c 2 Sections 9-3 / 9-4 Warm – Up: Simplify. Write each answer in standard form. 1. 6 h ( h 2 8 h 3) 3. w( w 1) 4 w( w 7) 2 2. y (2 y 3 7) 4. 6 x ( x 2) x (8 x 3) Objective: To multiply binomials Investigate binomial multiplication with “generic rectangles”. Example #1: Find each product. a) ( n 3)(7 n 4) b) (2 a 5)(6 a 1) Some pairs of binomials have special products. If you learn to recognize these pairs, finding the product of two binomials will sometimes be quicker and easier. Example #2: Difference of Squares Pattern Find each product. a) ( x 4)( x 4) b) (3 a 5 c )(3 a 5 c ) Example #3: Square of Binomial Pattern Find each product. a) ( n 7) 2 b) (6 p 2 r ) Example #4: Find the area of the shaded region. Simplify. a) 2 b) Each term of one polynomial must be multiplied by each term of the other polynomial. Example #5: Find each product. a) ( y 4)( 2 y 2 5 y 9) b) (5 c 2 c 3)(6 c 5) Closure Question: When multiplying two binomials, how is using the distributive property twice equivalent to using the FOIL method for multiplying? Sections 9-5 / 9-7 Warm – Up: Simplify each product. 1. ( x 2)( x 5) 2. ( a 4)( a 6) 3. ( n 7)( n 7) 4. ( y 3) Objective: To factor trinomials of the type ax 2 bx c 2 (where a = 1) Look at the warm-up problems to show the idea of factoring. (You need two numbers whose product is ac and whose sum is b) Example #1: Factor x 2 8 x 15 Example #2: Factor m 2 16 m 48 Example #3: Factor y 2 6 y 27 Example #4: Factor d 2 8d 9 Example #5: Difference of Two Squares Factor g 2 25 Example #6: Perfect Square Trinomials Factor n 2 20 n 100 Example #7: Factor x 2 11 xy 18 y 2 Closure Question: How can you determine what numbers are used in the binomial factors when factoring expressions of the type ax 2 bx c ? Sections 9-6 / 9-7 Warm – Up: Factor out the GCF. 1. 25 x 2 10 x 15 2. 24 a 3 32 a 2 8a Factor each expression. 3. y 2 11 y 24 Objective: To factor trinomials of the type ax 4. c 2 2 6 c 40 bx c (the leading coefficient is not 1) * Before factoring with two sets of parenthesis, first check to see if a GCF can be factored out. Example #1: Factor 3 x 2 5x 2 Example #2: Factor 2 k 2 21k 11 Example #3: Factor 5 w 2 6w 8 Example #4: Factor 6 n 2 19 n 15 Example #5: Difference of Two Squares Factor 25 a 2 64 Example #6: Perfect Square Trinomials Factor 4 c 2 36 c 81 Example #7: Factor 8 y 2 32 y 14 Example #8: Factor 18 d 3 12 d 2 6d Closure Question: What is the first thing you should look for when factoring a trinomial?