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Please add a bit more detail to each problem as to how the answers were derived. Thanks!

1. Perform the indicated operation: (x3 - 2x2 - 4x + 3)  (x - 3)
Since x3 - 2x2 - 4x + 3 = (x - 3) ( ), we have
(x3 - 2x2 - 4x + 3)  (x - 3) =
2. Find the product: (x - 2)(x + 3)(x - 4)
(x - 2)(x + 3)(x - 4) =
3. Simplify without having negative exponents: (- 3s-3t2)-2
(- 3s-3t2)-2
4. Convert to scientific notation and then solve. Give answer in scientific notation: (0.0000003)4
5. Factor completely: 3a3b - 3ab3
3a3b - 3ab3
6. Factor completely: ax - 2a - 5x + 10
ax - 2a - 5x + 10= (ax - 2a) -( 5x - 10)=a(x-2)-5(x-2)=(a-5)(x-2)
7. Solve: (2x - 1)(3x + 5) = 5
(2x - 1)(3x + 5) = 5>
So, x=5/6 or x=-2

8. The sum of two numbers is 4, and their product is -32. Write the complete solution (no guessing or trial by error) and find the numbers.
So, we have
x=-4 y=8
or x=8 y=-4.
So, two numbers are -4 and 8.
9. Perform the indicated operation and write the answer in lowest terms:

10. Perform the indicated operation and write the answer in lowest terms:

11. Simplify:

12. Solve:
Multiply by 2x(x-1), we have

So, x=2 or x=3

13. For a certain time period the ratio of the dollar value of exports to the dollar value of imports for the United States were 2 to 3. If the value of exports during that time period was 48 billion dollars, then what was the value of imports?

Solution. I Assume that the value of imports was x dollars. Then I have

So, the value of imports was 72 billion dollars

14. Simplify:

15. Simplify:

16. Simplify:

17. Find all real or imaginary solutions:

18. Solve by using the quadratic formula: 2x2 + 5x - 3 = 0

So, x=1/2 or x=-3

19. Solve by using the quadratic formula: 2x2 + 5x - 3 = 0

So, x=1/2 or x=-3

20. Graph the quadratic equation and state the domain and range: y = 16 - x2
The domain is R: all real numbers; the range is . Its graph is below.


(See attached file for full problem description)

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