2. ACTIVITY 41 Review For Final

3. Problem 17 Evaluate the expression:

4. Problem 83 Perform the indicated operations: Since there is no equal sign we find the LCD and the get each fraction over the LCD

6. Problems 45, 49, 55, 59 and 65: Factor the expressions: Can we factor 4x 2 +3 over the real numbers any further? This is equivalent to asking if there are any real roots, and the descrimate tell us this! Consequently, there are no real roots; therefore, no factor over the reals

8. possible rational zeros:

10. So we need only factor x 4 +x 2 +1 This does reduce further; however, we don’t have the tools to reduce this. So we have to look at the problem in a different way.

11. Problems 35, and 43 Find all real solutions of the following equations: Since there is an equal sign we find the LCD and multiply both sides by the LCD

14. Problem 75, and 83. Solve the following inequalities. Express the solution using interval notation an graph the solution set on the real number line.

15. Or

16. Problem 3 Consider the points P(–6, 2) and Q(4, –14) (a) Plot P and Q on the Coordinate plane. (b) Find the distance from P to Q.

17. Consider the points P(–6, 2) and Q(4, –14) (c) Find the midpoint of the segment PQ.

18. Consider the points P(–6, 2) and Q(4, –14) (d) Sketch the line determined by P and Q, and find its equation in slope-intercept form

20. Consider the points P(–6, 2) and Q(4, –14) (e) S ketch the circle that passes through Q and has center P, and fine the equation of this circle.

21. Problem 40 Find an equation for the line that passes through the point (1,7) and is perpendicular to the line x – 3y +16 = 0.

22. Problem 11 Show that the following equation represents a circle. Find its center and radius: x 2 + y 2 + 2x – 6y + 9 = 0

23. Problem 11: Solve the following system of equations: