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Various algegra problems

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Simplifying the folllowing expressions
3. (sqrt(x^3) + 3x)^2

5. The sixth term in the expansion of (2x - y)^8 is
6. Factor completely: x^4 - 3x^3 + 8x - 24
10. Rationalize the denominator: (x - 2)/(x - sqrt(x + 2))

11. solve for x: (3x + 4)/2 = 1 - x/3
12. solve for x(x - 3) = 4

13. (3 - 2i)^(-1)

14. solve: x^2 + 2x = -5
17. Find the solution set: |(2x - 5)/3| > = 3
20. How many liters of 50% alcohol solution must be added to 20 liters of a mixture that is 25% alcohol to obtain a 30% alcohol solution?
21. solve for x: x^4 + 2x^2 - 63 = 0
22. Find the solution set of 16x^2 = x^4.
23. The domain of the function defined by f(x) = sqrt(2x -x^2) is
24. if f(x) = 3x^2 - 5 and g(x) = 4x + 1, then (fg)(-1) =
25. if f(x) =x /(1 -x), then f^(-1)(x) is
26. which of the following equations does not define a one-to-one function?
27. An equation of the line with x-intercept 2 and y-intercept -3 is
28. The vertex of the parabola y = -x^2 - 2x + 8 is
29. The center, C, and the radius r of the circle x^2 + y^2 -4x + 2y = 4 are
30. When 4 - 5x^2 + 2x^3 is divided by x - 2, the remainder is
31. Counting multiplicites, the polynomial equation 3 - 5x + 3x^3 + x^4 = 0 has how many solutions?
32. The roots of the polynomial equation 2x^4 - 3x^3 + 19x^2 - 27x + 9 = 0 are
36. A logarithmic form of 2^y = x^3 /4 is
39. The maxtir is a triangular form of the augmented matrix associated with a particular system of equations. The system of equations has:
40. The determinant of the matrix is:

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Solution Preview

Please see the attached file for detailed solution.

1. (3)

Basic exponential function properties:

2. (4)

3. (2)

4.

So

5. Using the binomial theorem, the sixth term is

(2)

6. grouping and extracting the GCF

(2)

7. (4)

8. (5)

9. (5),
10. (1)

11. Multiply LCD, which is 6 to both sides:
Answer: (4)

12. (5), solving the equation by factoring:

13.
(1)

14.
By quadratic formula:

(2)

15. (5)

However, x - 3 is in the denominator, so
Therefore, there is no solution.

16.
Square both ...

Solution Summary

The solution covers various algebra aspects such as simplifying exponents and radical expressing, solving equations, roots of polynomials, functions, and system of equations, etc.

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