University:
East Georgia State College
Course:
MATH 1001 | Quantitative Skills & Reasoning
Academic year:

2021
Views:

259

Pages:

2
Author:

SpaceCadet101

Pre-Calculus Quiz 3.1-3.4 Review Name: Key Identify the zeros and their multiplicities (greater than one), and the y-intercept of the function. Then use end behavior and multiplicities to sketch a graph of the function. NO CALCULATOR!!! 1. P(x) = (x+1)(x+4)^2(x-2) Zeros: -1 mult 1; -4 mult 2; 2 mult 1 Y-Intercept: (0, -32) 2. P(x) = x^3 - 16x = x(x^2 - 16) = x(x+4)(x-4) Zeros: 0, 4, -4 all mult 1 Y-Intercept: (0, 0) Determine the end behavior of the polynomial function. NO CALCULATOR!!! 3. P(x) = -2x^3 - 3x^2 + 4x - 6 Down to the right Up to the left 4. P(x) = x^4 - 5x^3 + 9x^2 + 6x - 8 Up to the right Up to the left Divide the polynomials using long division. 5. (x^3 + 2x^2 + 11x + 2) / (x - 4) x^2 + 3x + 23 + 94/(x-4) 6. (x^3 + 2x^2 - 10) / (x + 3) x^2 - x + 3 - 19/(x+3) Divide the from #5 and #6 using synthetic division. 7. (x^3 + 2x^2 + 11x + 2) / (x - 4) x^2 + 3x + 23 + 94/(x-4) 8. (x^3 + 2x^2 - 10) / (x + 3) x^2 - x + 3 - 19/(x+3) Use the Remainder Theorem to evaluate P(c). 9. P(x) = 2x^3 - 9x^2 - 7x + 13; c = 5 P(5) = 3 10. P(x) = x^4 + 4x^3 + 7x^2 + 10x + 15; c = -3 P(-3) = 21 11. Find the remainder when x^301 - 6x^201 - x^2 - 2x + 4 is divided by x + 1. Remainder = 11 12. Use the Factor Theorem to show that x + 4 is a factor of P(x). P(x) = x^5 + 4x^4 - 7x^3 - 23x^2 + 23x + 12 P(-4) = -1024 + 1024 + 448 - 368 + 92 + 12 = 0 13. Find a polynomial of degree 3 with zeros 2, 3, and -1/2, and constant term 12. (x - 2)(x - 3)(2x + 1) = 2x^3 - 9x^2 + 7x + 6 To get a constant term of 12, multiply the equation by 2: 2x^3 - 18x^2 + 14x + 12 14. a) List all possible rational zeros: ±1, ±2, ±3, ±4, ±6, ±12 b) Find all real zeros: -1, 2, 3, -2 15. Evaluate the expression and write it in the form a + bi. a) (5 - 7i) - (12 + 2i) = -7 - 9i b) (2 - 3i)(1 + 4i) = 14 + 5i c) 6 / (4 - i) = 24/25 - 4i/25 d) √(-10) * √(-40) = -20 e) (3 - √(-12))(2 + √(-27)) = 24 + 5√3i 16. Solve the equation. Use the Quadratic Formula. a) x^2 - 4x + 5 = 0 x = 2 ± i b) x^2 + x + 1 = 0 x = (-1 ± i√3) / 2