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# Basic Algebra (45 Problems)

1. Express the following product powers of t as a single power of t

2. Write without parenthesis

3.

4. Simplify without negative exponents

5. Simplify without negative exponents

6. Multiply and simplify
(4z - 2u - 2)(6z - 5u + 6)

7. Write in simplest form without parentheses
(z - 5)(z + 7)

8. Factor Completely

9. Factor

10. Factor
tu - 5w - 5u + wt

11. Find the roots of quadratic equation

12. Solve for w

13. Solve for u (Simplify)

14. Multiply and write in lowest terms

15. Express in lowest terms

16. Subtract and write in lowest terms

17. Write as a single rational expression

18. Reduce to lowest terms

19. Solve for x (Simplify)

20. Find all values of u.

21. Solve proportion for x.

22. Simplify

23. Rewrite in simplified radical form and assume all variables represent positive numbers

24. Write in simplified radical form

25. Simplify in lowest terms

26. Simplify and assume variables represent positive real numbers

27. Write in simplified radical form by rationalizing denominator

28. Solve for u, where u is a real number

29. Solve for x (Simplify)

30. Solve where x is a real number (Simplify)

31. Simplify

32.

33. Write answer in standard form

34. Find value of k such that of a perfect square

35. Solve x by using quadratic formula

36. Find all real or imaginary roots of

37. Factor

38. When a ball is thrown, its height in meters h after t seconds is given by the equation
where v is the initial upwards velocity in meters per second. If v=10 meters per second, find all values of t for which h=3 meters.

39. Need the vertex and 4 additional points of

40. Find x-intercepts and coordinates of the vertex for the parabola

41. Factor Completely

42. Graph the set

43. Find the slope
(-21,5)(9,-10)

44. Greatest Common Factor

45.

46. Factor Completely

#### Solution Preview

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1. Express the following product powers of t as a single power of t

=

2. Write without parenthesis

3.

Solution.

4. Simplify without negative exponents

=

5. Simplify without negative exponents

6. Multiply and simplify
(4z - 2u - 2)(6z - 5u + 6)

7. Write in simplest form without parentheses
(z - 5)(z + 7)

8. Factor Completely

9. Factor

10. Factor
tu - 5w - 5u + wt

11. Find the roots of quadratic equation

Solution. As , from we know that

So,
w=-7 or w=3

12. Solve for w

Solution. As , we have

i.e.,
(w-5)(w+1)=0

So, w=5 or w=-1

13. Solve for u (Simplify)

Solution. As , we have
2=-4u
So,
u= -2/4
=-1/2

14. Multiply and write in lowest terms

15. Express in lowest terms

16. Subtract and write in lowest terms

17. Write as a single rational expression

18. Reduce to lowest terms

19. Solve for x (Simplify)

Solution. We have

So,
...

#### Solution Summary

Forty-five basic algebra problems are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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