University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2019
Views:

431

Pages:

4
Author:

StellarStrategist

(5x³ - 13x² - x + 2) ÷ (x² - 3x + 1) x² - 3x + 1 | 5x³ - 13x² - x + 2 -(5x³ - 15x² + 5x) -------------------- 2x² - 6x + 2 -(2x² - 6x + 2) -------------------- 0 **Answer:** 5x + 2 2. (x⁴ + 3x² + 2) ÷ (x² - 1) x² + 0x - 1 | x⁴ + 0x³ - 3x² + 0x + 2 -(x⁴ + 0x³ - x²) -------------------- -2x² + 0x + 2 -(-2x² + 0x + 2) -------------------- 0 **Answer:** x² - 2 **II. Divide the polynomials using synthetic division.** 1. (2x³ + 2x² - x + 2) ÷ (x - 1/2) 1/2 | 2 2 -1 2 | 1 1.5 0.25 -------------------- 2 3 0.5 2.25 **Answer:** 2x² + 3x + 1/2 + 9/4(x - 1/2) 2. (3x³ - 10x² + 12x - 22) ÷ (x - 4) 4 | 3 -10 12 -22 | 12 8 80 3 2 20 58 **Answer:** 3x² + 2x + 20 + 58/(x - 4) **III. Use synthetic division to evaluate each function.** 1. Given f(x) = 4x³ - 13x + 10. Find f(8). 8 | 4 0 -13 10 | 32 256 1944 4 32 243 1954 f(8) = 1954 **IV. Use synthetic division to show that the given binomial is a factor.** 1. g(x) = x⁴ - 11x³ + 41x² - 61x + 30 factor (x - 5) 5 | 1 -11 41 -61 30 | 5 -30 55 -30 1 -6 11 -6 0 x - 5 is a factor **V. Use the Rational Zero Test to determine the set of possible rational zeros.** 1. f(x) = 2x⁴ - 17x³ + 35x² + 9x - 45 Possible rational zeros: ±1, ±3, ±5, ±9, ±15, ±45 ±1/2, ±3/2, ±5/2, ±9/2, ±15/2, ±45/2 **VI. Write a polynomial function, given the zeros of the function.** 1. x = [-3, 3, 4] (x - 3)(x + 3)(x - 4) (x² - 9)(x - 4) f(x) = x³ - 4x² - 9x + 36 2. x = [-6, -1, 2, 3] (x - 6)(x + 1)(x - 2)(x - 3) (x² + 5x - 6)(x² - 5x + 6) x⁴ - 10x³ + 25x² - 30x - 36 f(x) = x⁴ - 10x³ + 25x² - 30x - 36