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DVM 0071 Elementary Algebra Review of Module 5 Objectives: Mastering Polynomials & Integer Exponents 5.1 Simplify basic algebraic expressions that involve using the distributive property. Simplify the following expressions 5.2 a) 3a – 5(b – 2) b) (3k + 1) – (4 – k) c) -4x(3x – 7y2 + 4) d) -7.1(3r +7) + 3.5(10r + 10) Evaluate algebraic expressions, given the values of the variables. a) 5x2 -5x + 4y for x = ¾ and y = -1.5 b) (3x – 2)2 + 1 for x = -4 c) 1 h(b1 + b2) 2 when b1=2, b2=4, and h=8 5.3 Find square roots (exact, rounded using a calculator, and estimate without a calculator). a) Estimate the value of b) Find the value of c) Find the value of to one decimal place without a calculator without a calculator. rounded to thousandths. Module 5 Objectives: DVM 0071 Mastering Polynomials & Integer Exponents 5.4 Apply the rules of exponents to simplify expressions involving integer exponents. a) Simplify: (4x)3 (2x2)4 x2 y3 b) Simplify: 4 x 3y 4 c) Simplify: z 5 d) Simplify: x x2 x3 y y y2 e) Simplify: (2x)0 f) Simplify: (2x23y3)2 g) Simplify: [(a)-6]-3 h) Simplify: ( x)2 5.5 Apply the basic operations to polynomials (monomial division only). a) Add: 6x 4 2x 3 7x 2 b) Subtract: 3x 2 4x c) Multiply: x 2 2x 5 and 7 from 2x 2 3 by 4x 3 d) Multiply, using FOIL: 3x 4 9x 4x 2 11 7 7x 7a 3b 5a Review of Module 5 Objectives: DVM 0071 2x 3 5b 2 Module 5 Objectives: DVM 0071 Mastering Polynomials & Integer Exponents e) Expand the following: 3y f) Multiply the binomials: 3p g) Expand the following: 4a 2 4z 4 3p b 4 3 h) Divide and Simplify: (16x4 – 8x2 + 12x)/(-3x8y3z) 5.6 Convert numbers between scientific and standard notation. Solve application problems in scientific notation. 1) 2) Write the numbers in scientific notation or standard form. a) 295,060,000 write in scientific notation b) -9.105×10-7 write in standard form c) (5×103)(2.3×10-7) write in standard form Use Scientific Notation to solve applied problems a) Light travels 300,000,000 meters per second. A light year is the distance that light travels in one year. Use scientific notation to express the number of meters traveled in one light year. b) If E= Energy emitted by an oscillation and V=frequency of oscillation, then E=kV where k Plank’s constant 6.626×10-24J. Find E if V= 1.25 ×1015 in J (Joules). Review of Module 5 Objectives: DVM 0071 3