Chapter 8 Class Notes Alg. 1H 8-A1 (Lessons 8-1&8-) Monomials and Factoring p. 40-4 Prime Factorization: a whole number epressed as the of factors. Tree Method: Ladder Method: Factored Form of a Monomial: epressed as the product of and ; o no variable has an greater than. 1A) 38rs t 66 pq 3 3 18 y Greatest Common Factor: : the of the factors; the greatest number that is a factor of original numbers. Relatively Prime: when or more integers or monomials have a GCF 3A) of 3 17 d ; 5d p q; 3 pr t 7 a b; 15ab c Ch. 8 Notes Alg. 1H 1
Factoring Using the Distributive Property p. 46-49 Factor a Polynomial: find its factored form. Use the ab ac a b c ab ac a b c 1A) 16a 4b 15 5 3 9 36 p q pq pq D) 1y 4y 30 y 4 (p. 48) Zero Product Property: If the of factors is 0, then at least 1 of the factors must be equal to. Solve a Polynomial Equation: Read E. 4 1. Set the polynomial =.. completely 3. Determine the values of the variable that would make factor equal. (Solutions are also called.) 4A) 3nn 0 7d 35d 0 10 Ch. 8 Notes Alg. 1H
(p. 47) When a polynomial has 4 or more terms, factor by of terms. E.) y 7 4y 14 A) rs 5s r 5 6 15 8 0 1 15 16 0 a ab a b Additive Inverses: Binomials that have opposite signs on each term. EX: 7 y and y 7 10 and 10 1 y 7 3A) c cd 8d 4 3p p 18p 7 Summary: Factor by Grouping 1. Use when there are or more terms.. Terms with can be grouped together. 3. The common binomial factors are or. 4. Algebraic Model: a b ay by a b y a b a b y or y a b Ch. 8 Notes Alg. 1H 3
8-A (Lesson 8-3) Factoring Trinomials: b c p. 434-437 When are multiplied, each binomial is a of the product. Factoring is like unwrapping the foil start with the and figure out what the factors are. Eamples: A. 3 C. 8 B. 5 6 1A) a 8a 15 9 10t t A) 1 m m s 11s 8 3A) h 3h 40 r r 4 Ch. 8 Notes Alg. 1H 4
Solve Equations by Factoring: 1. Write the trinomial as an equal to.. completely. 3. Use the to find the solutions. 4. The solutions are also called. 4A) 16 8 g 6g 7 15 p. 437 #5 Check Your Progress p. 437 #7,9,11 Check Your Understanding Ch. 8 Notes Alg. 1H 5
8-A3 (Lesson 8-4) Factoring Trinomials: a b c p. 44-443 Guess and Check Method: possibilities. Check for correct term E. A) 6 7 5 11 6 Practice will pay off! You will get better at this, and it will take less guesses before you find the correct factors! 1A) 5 13 6 4 3 Always check for a BEFORE factoring a trinomial! 10y 35y 30 D) 6 8 Ch. 8 Notes Alg. 1H 6
Prime Polynomial: cannot be. A) 4r r 7 3 5 Solve Equations by Factoring: 1. Write the trinomial as an equal to.. completely. 3. Use the to find the solutions. (The solutions are also called.) 3A) 3 5 1 30 88 0 6 5 13 Ch. 8 Notes Alg. 1H 7
8-A4 (Lesson 8-4) Vertical Motion Model p. 444 h 16t vt s h = ending o in feet v = initial o speed and direction positive or negative o feet per second) s = height o in feet t = o in seconds o usually is the unknown value you have to figure out Model: Read E. 4 Pep Rally and do CYU #10 Cliff Diving Check Your Progress (under E. 4) Ch. 8 Notes Alg. 1H 8
8-A6 (Lesson 8-5) Factoring Differences of Squares p. 447-450 Difference of Squares: a b a b a b EX: 9 3 3 or 3 3 1A) 81 t 64g h 3 9 4 D) 3 4y 9 y Solve: E) 9t 49 0 F) 11 100 0 Sometimes you have to apply the Difference of Squares Pattern more than to factor a polynomial. A) 4 4 65 y 1 16a 16b 4 4 Use Several Factoring Techniques: 3A) 3 50 5 3 r r r 6 11 66 4) Solve: 3 18 50 5) Ch. 8 Notes Alg. 1H 9
8-A7 (Lesson 8-6) Perfect Squares and Factoring p. 454-458 Review: Read p. 404-405, Key Concepts and E. 1 and. Perfect Square Trinomial: a ab b a b a ab b a b E: 4 0 5 5 1. The 1 st term must be a.. The middle term must be the product of the square roots of the and terms. 3. The last term must be a. 1A) n 4n 144 9 81 5 30 9 D) y 8y 16 A) 3 9t 3t 0 p. 456 E. 3 Solving: 3A) a 1a 36 0 4 4 y y 0 3 9 16 64 0 D) 4y 36y 81 0 Ch. 8 Notes Alg. 1H 10
p. 457 Square Root Property: If n, then n E.: Use this property to solve the following equations: 4) h 16t h0 (The bridge is 100 ft. high.) 9 9 3 5A) z z 1 16 y 8 7 p. 455 Concept Summary: Factoring Polynomials # of Factoring Technique Terms or more 3 Difference of Squares Perfect Square Trinomial Leading coefficient is 1 Leading coefficient is not 1 Greatest Common Factor Eample 4 or more Grouping Ch. 8 Notes Alg. 1H 11
8-A8 Area and Vertical Motion Word Problems (Power Point) A. Geometry Problems: It helps to draw a sketch! 1. A triangle has an area of 40 cm. Find the height, h, of the triangle.. The length of a rectangular swimming pool is 0 ft. greater than its width. The area of the pool is 55 ft. What are its dimensions? 3. Four squares, each with side, are cut from a square piece of paper as shown. What value of will result in an area that is 7 of the 16 original area? B. Vertical Motion Problems: Learn the Formula! 4. While standing on the roof of a building that was 400 ft high, you dropped an egg. How many seconds will it take the egg to hit the ground? Ch. 8 Notes Alg. 1H 1
5. How long would it take a hammer to hit the roof of a truck if the hammer were dropped from a height of 70 ft? The roof of the truck is 6 ft high. 6. A rocket is launched from ground level at an initial velocity of 100 feet per second. How many seconds will it take for the rocket to return to the ground? 7. A football is kicked upward at a velocity of 4 ft per second (ft/s). When will it reach a height of 0 ft? 8. A soccer player kicks a soccer ball with a velocity of 3 ft/sec. If the ball reaches a height of 16 ft, how long does it stay in the air? Ch. 8 Notes Alg. 1H 13