MATH 157 Final: 100q4 sol

Add and subtract the polynomials and simplify: 7. (5x 2 + 6x-2)+(3x-2x+ 4) 8. (4x2-7x+1)-(x+9x-2) 9. (3x 2 + 2x + 8) + (9x2+7x -1) 10. (2x 2-5x -3) -(6x2-4x-8) 11. (7x-3) +(5x-4) 12. (2x+ 6)-(8x+9) Multiply the polynomials and simplify: 13. (7x 3-89(9/ + 5x-x) 14. (5x 3) (6x2+ 2x-9) 15. (10x+ 7) (6x-8) 16. (9x+ 4) (3x2-1) 17.(8x 3-2x2+ 3x) (Bx 2+ 7x-5) Solve each quadratic equation through factoring: 18, x 2 + 4x + 4 = 0 19. x2-14x+49 0 20. y2+ 7y-60 0 21. Ñ (x-3)-18 22, x 2 = 12x-36 23. 5x 2 20x

Find all solutions of the equation 3x - 7 = 4 = 0. Explain why you have found all the roots. Discuss this problem in class. Find all solutions of the quadratic equations x^2 + x --4 = 0. Explain why you have found all the roots. Discuss this problem in class. Apply the quadratic formula to the equation x^2 + x + 4. What difficulty do you encounter? Does this equation have any real roots? Draw the graph of p(x) = x^2 + x + 4 and discuss in class why there are no real roots. If a polynomial is to have real roots then its graph must cross the x-axis. Discuss in class why this is true. Then discuss why a cubic equation will always have at least one real root while a quadratic equation may not. Discuss in class whether a quartic (i.e., a fourth-degree) equation will always have a real root. Look at some examples. What about p(x) = x^4 + 1? What about x^4 - 2x^2 + 1? Use Cardano's method to find a root of the polynomial x^3 - x - 6. Use Cardano's method to find a root of the polynomial 3x^3 - 10x^2 + 9. Can you write down a polynomial whose roots are -1, 3, 5? Can you give an example of a polynomial of degree 2 that has no real roots? How about degree 4? Explain why a polynomial of odd degree at least 1 will always have at least one real root.

Graph each line by hand, finding intercepts to determine two points on the line. 27. x-y=4 28, x + y = 4 29. 3x-y = 6 Exercises 30. 2x - 3 6 1. 2 Sy 10 2. 4x 3y-9 A line having an equation of the form" kx, where k is a real number, k + 0, will always pass through the origin. To graph such an equation by hand, we can determine a second point and then join the origin and that second point with a straight line. Use this method to graph each line. 33, y = 3r 34, y =-2x 35. y =-0.75x 36, y Copyright © 2011, 2007, 2003, 1999, 1996 Pearson Education, Inc. | Legal Terms