Chapter 8 Class Notes 8-A1 (Lessons 8-1&8-2) Monomials and Factoring p Prime Factorization: a whole number expressed as the of factors.

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1 Chapter 8 Class Notes Alg. 1H 8-A1 (Lessons 8-1&8-) Monomials and Factoring p 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 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

2 Factoring Using the Distributive Property p Factor a Polynomial: find its factored form. Use the ab ac a b c ab ac a b c 1A) 16a 4b 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 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

3 (p. 47) When a polynomial has 4 or more terms, factor by of terms. E.) y 7 4y 14 A) rs 5s r 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

4 8-A (Lesson 8-3) Factoring Trinomials: b c p 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 A) a 8a t t A) 1 m m s 11s 8 3A) h 3h 40 r r 4 Ch. 8 Notes Alg. 1H 4

5 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

6 8-A3 (Lesson 8-4) Factoring Trinomials: a b c p Guess and Check Method: possibilities. Check for correct term E. A) Practice will pay off! You will get better at this, and it will take less guesses before you find the correct factors! 1A) Always check for a BEFORE factoring a trinomial! 10y 35y 30 D) 6 8 Ch. 8 Notes Alg. 1H 6

7 Prime Polynomial: cannot be. A) 4r r 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) Ch. 8 Notes Alg. 1H 7

8 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

9 8-A6 (Lesson 8-5) Factoring Differences of Squares p Difference of Squares: a b a b a b EX: or 3 3 1A) 81 t 64g h D) 3 4y 9 y Solve: E) 9t 49 0 F) Sometimes you have to apply the Difference of Squares Pattern more than to factor a polynomial. A) y 1 16a 16b 4 4 Use Several Factoring Techniques: 3A) r r r ) Solve: ) Ch. 8 Notes Alg. 1H 9

10 8-A7 (Lesson 8-6) Perfect Squares and Factoring p Review: Read p , Key Concepts and E. 1 and. Perfect Square Trinomial: a ab b a b a ab b a b E: 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 D) y 8y 16 A) 3 9t 3t 0 p. 456 E. 3 Solving: 3A) a 1a y y D) 4y 36y 81 0 Ch. 8 Notes Alg. 1H 10

11 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.) A) 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

12 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

13 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