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Factoring Polynomials to Prime

Attached is a math study review.

1. Factor completely, or state that the polynomial is prime.
2x3 + 250

2. Factor completely, or state that the polynomial is prime.
16x3 - 16x

3. Factor completely, or state that the polynomial is prime.
9x4 - 9

4. Factor by grouping. Assume any variable exponents represent whole numbers.
x3 + 9x - 4x2 - 36

5. Factor by grouping. Assume any variable exponents represent whole numbers.
3x3 - 6x2 + 7x - 14

6. First, write the value(s) that make the denominator(s) zero. Then solve the equation.

7. Solve the equation.

8. Find the product and write the result in standard form.
(9 + 4i)(9 - 8i)

9. Solve the polynomial equation by factoring and then using the zero product principle.
x3 + 9x2 + 20x = 0

10. Solve the radical equation, and check all proposed solutions.
= x + 3

11. Solve the absolute value equation or indicate that the equation has no solution.

12. Solve the equation by the square root property.
2x2 = 26

13. Solve the equation by the square root property.
(x - 6)2 = 16

14. Solve the equation by expressing each side as a power of the same base and then equating exponents.

15. Solve the equation by expressing each side as a power of the same base and then equating exponents.

16. Solve the exponential equation. Express the solution set in terms of natural logarithms.

17. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.
log2(x + 2) + log2(x - 4) = 4

18. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.
log6(x - 3) = 2

19. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.
log3(x + 5) = 2 + log3(x - 1)

20. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.
log9(6x + 2) = log9(6x + 7)

21. Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

22. Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

23 Use properties of logarithms to write as a single logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

24. Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots.
2x3 - 13x2 + 22x - 8 = 0

25. Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots.
3x4 - 19x3 + 69x2 - 99x + 26 = 0

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Solution Summary

Twenty-five problems involving the factoring of polynomials are solved.

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