University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2024
Views:

396

Pages:

2
Author:

5CelestialChronicle

Name: Key Honors Pre-Calculus Quiz Review 2.1-2.4 (worksheet & book) Sketch the graph by finding the zeros (use the rational zero theorem) and by evaluating the end behavior. 1. f(x) = -3x³ - 2x² + 27x + 18 P: 18 (1, 2, 3, 6, 9, 18) q: 3 (1, 3) p/q: ±1, ±2, ±3, ±6, ±9, ±18, ±1/3, ±2/3 -3 | -3 -2 27 18 | 9 -21 -18 ----------------------- -3 7 6 0 L. coeff. = -3 (3x² + 7x + 6) (3x + 2)(x + 3) 2. Use long division to divide (x⁴ - 3x² + 2) ÷ (x² - 1) x² + 0x - 1 | x⁴ + 0x³ - 3x² + 0x + 2 -(x⁴ + 0x³ - x²) -------------------- -2x² + 0x + 2 -(-2x² + 0x + 2) -------------------- 0 Q(x) = x² - 2 3. Use synthetic division to divide (2x³ + 6x² - 14x + 9) ÷ (x - 1) 1 | 2 6 -14 9 | 2 8 -6 -------------------- 2 8 -6 3 2x² + 8x - 6 + 3/(x-1) 4. Given one factor find all the zeros. (Do not use a graphing calculator) (x⁴ - 4x³ - 22x² + 7x + 24) if (x+2) is a factor -2 | 1 -4 -22 7 24 | -2 12 -20 -14 -------------------- 1 -6 -10 -13 10 try again for root -2 | 1 -6 -10 -13 10 | -2 16 -12 50 -------------------- 1 -8 6 -25 60 try again for root -2 | 1 -8 6 -25 60 | -2 20 -52 154 -------------------- 1 -10 26 -77 214 (x-3)(x-4) x = 3, 4, -1, -2 5. Find all the zeros of the polynomial: f(x) = 2x⁴ + 7x³ - 26x² + 23x - 6 (Answers must be exact...no decimal answers!) ±1, ±2, ±3, ±6, ±1/2, ±3/2 2 | 2 7 -26 23 -6 | 4 22 -8 30 -------------------- 2 11 -4 15 0 2x² + 11x - 6 = 0 (2x-1)(x+6) = 0 x = 1/2, -6, 1 (Double Root) Name: Honors Pre-Calculus Quiz Review 2.1-2.4 (worksheet & book) Simplify the following complex numbers: 6. (-8-3i)-(-8+5i) -8-3i+8-5i = 0-8i or -8i 7. (-1-4i)(2+3i) -2-3i-8i-12i² -2-11i+12 10-11i 8. (-16+3i)-(25-2i) -16+3i-25+2i -41+5i 9. (3+2i)/(5-i) (3+2i)(5+i)/(5-i)(5+i) 15+3i+10i+2i² / 25-i² 13+13i / 26 1/2 + 1/2i 10. (6+i√2)/(6-i√2) (6+i√2)(6+i√2)/(6-i√2)(6+i√2) 36+6i√2+6i√2+2i²/36-2i² 36+12i√2+2i²/38 17+6√2/19 = 17/19 + 6√2/19i 11. Plot the complex number on the complex plane: (-4+2i) 12. Graphing Calculator problem: A textile manufacturer has daily production costs of C = 10,000 - 110x + 0.45x³, where C is the total cost and x is the number of units produced. Determine how many units should be produced each day to yield a minimum cost? 1 1. What is the minimum cost? x = -b/2a = 110/(2*(0.45)) = 122 units C(122) = 10,000 - 110(122) + (0.45)(122)³ = $3277.80