Algebra Name: Date: Period: # Exponents and Polynomials (1) Page 453 #22 59 Left (2) Page 453 #25 62 Right (3) Page 459 #5 29 Odd (4) Page 459 #14 42 First Column; Page 466 #3 27 First Column (5) Page 459 #15 43 Second Column; Page 466 #6 30 Fourth Column (6) Page 459 #16 44 Third Column; Page 466 #31 47 Left (7) Page 459 #17 45 Right; Page 466 #33 48 Third Column (8) Page 473 #16 44 Left *******Quiz Tomorrow******** (9) Page 580 #19 55 Left Every Other One (10) Page 580 #21 52 Right Every Other One (11) Page 587 #9 45 Left (12) Page 587 #10 46 Middle (13) Page 587 #11 47 Right *******Quiz Tomorrow******* (14) Page 593 #16 40 Every Other Even (15) Applications of Area Problems (16) Practice Test for Test Tomorrow (17) Page 498 #1 10; Page 638 #1 7
8.1 Multiplication Properties of Exponents (R,E/2) Steps and Laws for Exponents 1. Power to Power - Look for an exponent on the outside of parenthesis i. Multiply the Exponents 2. Multiplying Monomials Look for two terms being multiplied together i. Multiply the Coefficients ii. Re-write the Variables iii. Add the Exponents 3. Dividing Monomials Look for a fraction bar i. Divide the Coefficients ii. Re-Write the Variables iii. Subtract the Exponents Down 4. Combining Like Terms Look for a + or sign between two terms i. Combine the Coefficients ii. Re-write the variable and exponent Never: - Leave an answer in simplest form with a negative exponent (negative exponent property). - Leave an answer in simplest form with a zero as an exponent (zero exponent property E1) a. 5 3 5 6 b. x 2 x 3 x 4 c. 3 3 5 d. (-2)(-2) 4 P1) a. 4 5 4 3 b. y 3 y 4 y 5 c. 2 2 6 d. (-5)(-5) 3 E2) a. (3 5 ) 2 b. (y 2 ) 4 c. [(-3) 3 ] 2 d. [(a+1) 2 ] 5 P2) a. (5 2 ) 3 b. (x 3 ) 2 c. [(-2) 3 ] 4 d. [(a-2) 3 ] 2 E3) a. (6 5) 2 b. (4yz) 3 c. (-2w) 2 d. (2w) 2 P3) a. (3 4) 2 b. (3xy) 4 c. (-3y) 2 d. (3y) 2 E4) Simplify (4x 2 y) 3 x 5 P4) Simplify (3x 4 y) 2 y 5
8.2 and 8.3 Zero and Negative Exponents, Division Property of Exponents (R,E/4) Steps and Laws for Exponents 1. Power to Power - Look for an exponent on the outside of parenthesis i. Multiply the Exponents 2. Multiplying Monomials Look for two terms being multiplied together i. Multiply the Coefficients ii. Re-write the Variables iii. Add the Exponents 3. Dividing Monomials Look for a fraction bar i. Divide the Coefficients ii. Re-Write the Variables iii. Subtract the Exponents Down 4. Combining Like Terms Look for a + or sign between two terms i. Combine the Coefficients ii. Re-write the variable and exponent Never: - Leave an answer in simplest form with a negative exponent (negative exponent property). - Leave an answer in simplest form with a zero as an exponent (zero exponent property E1) a. 2-2 b. (-2) 0 c. 5 -x d. ( ) e. 0-3 P1) a. 3-4 b. (-5.2) 0 c. 4 -y d. ( ) e. 0-1 E2) a. 5(2 -x ) b. 2x -2 y -3 P2) a. 4(3 -k ) b. 5g -3 h -4 E3) a. 3-2 3 2 b. (2-3 ) -2 c. 3-4 P3) a. 4-3 4 3 b. (5-2 ) -3 c. 2-3
E4) a. (5a) -2 b. P4) a. (4y)-3 b. E5) a. b. c. d. P5) a. b. c. d. E6) a. ( ) b. ( ) c. ( ) P6) a. ( ) b. ( ) c. ( ) E7) a. b. ( ) P7) a. b. ( )
8.4 Scientific Notation (Multiply and Divide w/ Calculator) (I,E/1) A number is written in if it is of the form c x 10 n, where 1 c < 10 and n is an integer. E1) Rewrite in decimal form. a. 2.834 x 10 2 b. 4.9 x 10 5 c. 7.8 x 10-1 d. 1.23 x 10-6 P1) Rewrite in decimal form. a. 3.128 x 10 3 b. 6.4 x 10 4 c. 3.9 x 10-1 d. 6.12 x 10-5 E2) Rewrite in scientific notation. a. 34,690 b. 1.78 c. 0.039 d. 0.000722 e. 5,600,000,000 P2) Rewrite in scientific notation. a. 52,314 b. 3.2 c. 0.0471 d. 0.0000428 e. 602,000,000 E3) Evaluate the expression. Write the result in scientific notation. a. (1.4 x 10 4 )(7.6 x 10 3 ) b. (1.2 x 10-1 ) (4.8 x 10-4 ) c. (4.0 x 10-2 ) 3 P3) Evaluate the expression. Write the result in scientific notation. a. (2.5 x 10 4 )(5.8 x 10 2 ) b. (1.82 x 10-1 ) (1.4 x 10-3 ) c. (1.5 x 10-4 ) 3 E4) Use a calculator to multiply 0.000000748 by 2,400,000,000. P4) Use a calculator to multiply 0.00000052 by 3,500,000,000.
10.1 Add and Subtract Polynomials (I,E/2) An expression which is the sum of terms of the form ax k where k is a nonnegative integer is a. Polynomials are usually written in for, which means that the terms are placed in descending order, from largest degree to smallest degree. Polynomial in standard form 2x 3 + 5x 2 4x + 7 Leading coefficient Constant term The of each term of a polynomial is the exponent of the variable. The is the largest degree of its terms. When a polynomial is written in standard form, the coefficient of the first term is the. A polynomial with only one term is called a. A polynomial with two terms is called a. A polynomial with three terms is called a. E1) Identify the coefficients of -4x 2 + x 3 + 3 P1) Identify the coefficients of 4 x + 2x 3 E2) Degree Polynomial Degree Classified By Degree a. 6 b. -2x c. 3x + 1 d. x 2 + 2x - 5 e. 4x 3 8x f. 2x 4 7x 3 5x + 1 Classified By Number Of Terms P2) Polynomial Degree Classified By Degree a. -5 b. (1/4)x c. -9x + 1 d. x 2-6 e. -x 3 + 2x + 1 f. 3x 4 +2x 3 x 2 +5x -8 Classified By Number Of Terms
E3) Find the sum. Write the answer in standard form. a. (5x 3 x + 2x 2 + 7) + (3x 2 + 7 4x) + (4x 2 8 x 3 ) b. (2x 2 + x 5) + (x + x 2 + 6) P3) Find the sum. Write the answer in standard form. a. (-8x 3 + x - 9x 2 + 2) + (8x 2 2x + 4) + (4x 2 1 3x 3 ) b. (6x 2 - x + 3) + (-2x + x 2-7) E4) Find the difference. Write the answer in standard form. a. (-2x 3 + 5x 2 x + 8) ( -2x 3 + 3x 4) b. (x 2 8) (7x + 4x 2 ) c. (3x 2 5x + 3) (2x 2 x 4) P4) Find the difference. Write the answer in standard form. a. (-6x 3 + 5x 3) ( 2x 3 + 4x 2 3x + 1) b. (4x 2 1) (3x - 2x 2 ) c. (12x 8x 2 + 6) (-8x 2 3x + 4)
10.2 Multiply Polynomials (I,E/3) E1) Find the product (x + 2)(x 3) P1) Find the product (x + 8)(x 7) E2) Find the product (3x - 4)(2x + 1) P2) Find the product (2x +3)(5x + 1) E3) Find the product (x 2)(5 + 3x x 2 ) P3) Find the product (x 4)(5x + 9 2x 2 ) E4) Find the product (4x 2 3x 1)(2x 5) P4) Find the product (5x 2 x 3)(6x 5)
10.3 Special Products of Polynomials (I,E/1) Special Product Patterns Factored Form (General) Product Form (General) Factored Form (Example) Product Form (Example) (a + b)(a b) a 2 b 2 (3x 4 )(3x + 4) 9x 2-16 (a + b) 2 a 2 + 2ab + b 2 (x + 4) 2 x 2 + 8x + 16 (a b) 2 a 2 2ab + b 2 (2x 6) 2 4x 2 24x + 36 E1) Find the product (5t 2)(5t + 2) P1) Find the product (3b 5)(3b + 5) E2) Find the product P2) Find the product a. (3n + 4) 2 b. (2x 7y) 2 a. (7a + 2) 2 b. (2p 5q) 2 E3) Use mental math to find the product P3) Use mental math to find the product a. 17 23 b. 29 2 a. 19 21 b. 38 2
Exponent Applications (Including Area) (I,E/1) E1) Find an expression for the area of the shaded region. 1 x 1 3 x 3 E2) Find an expression for the area of the shaded region. 1 x 1 3 x 3 E3) Keng creates a painting on a rectangular canvas with a width that is four inches longer than the height, as shown in the diagram below. h h+4 a. Write a polynomial expression, in simplified form, that represents the area of the canvas. b. Keng adds a 3-inch-wide frame around all sides of his canvas. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame. c. Keng is unhappy with his 3-inch-wide frame, so he decides to put a frame with a different width around his canvas. The total area of the canvas and the new frame is given by the polynomial h 2 + 8h + 12, where h represents the height of the canvas. Determine the width of the new frame. Show all work and explain each step.