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Basic Algebra

Please see attached file for the properly formatted problems.....

1. Simplify. (m^4)^3(m^2)^9
_______________
(m^3)2^

2. Write in descending-exponent form, and give the degree.
4x3 - 6x4 - 6

3. Find the value of the polynomial x3 - 4x when x = -2.

A) -2 B) 0 C) 2 D) 14

4. Write 0.041 in scientific notation.

5. Divide. Write the answer in scientific notation.

6. Add 7y2 - 4y - 1 and 3y2 - 9y + 5.

7. Remove the parentheses and simplify. 8a - (10a - 3b)

8. Subtract 2x - 3x2 + 5x3 from 5x3 + 4x - x2.

9. Multiply. 3xy2(5xy - 4x + 6y)

10. Multiply. (x + 2)(x - 2)

A) x2 - 4x - 4 B) x2 + 4 C) x2 + 4x - 4 D) x2 - 4

11. Multiply.

12. Divide.

13. Divide.

14. Find the greatest common factor. 16b2, 40b5, 64b10

15. Factor. 8m4n - 16mn4

16. Factor. 4x(x + 6y) + 6(x + 6y)

17. Factor completely. 6z3 - 27z2 + 12z

A) z(6z - 1)(z - 12) C) 6z(z - 1)(z - 12)
B) 3z(2z - 1)(z - 4) D) 2z(3z - 1)(z - 4)

18. Factor by grouping. 24x3 + 6x2 - 4x - 1

19. Factor completely. y4 + 3y3 - 5y2 - 15y

20. State which method should be applied as the first step for factoring the polynomial.
6x3 + 9x

A) Find the GCF.
B) Group the terms.
C) Factor the difference of squares.
D) Use the ac method (or trial and error).

21. Factor completely. 5a2 - 125

A) 5(a + 5)(a - 5) B) 5(a - 5)2 C) 5a(a - 25) D) (5a - 1)(a - 125)

22. The product of two consecutive positive even integers is 360. Find the integers.

23. The profit on a watch is given by P = x2 - 13x - 80, where x is the number of watches sold per day. How many watches were sold on a day when there was a $50 loss?

A) 13 B) 14 C) 15 D) 16

24. Factor completely. 3(x - 2)2 - 3(x - 2) - 6

A) 3(x - 4)(x - 1) B) 3(x - 4)(x + 1) C) 3(x - 2)(x - 1) D) 3(x - 2)(x + 1)

25. Is the following binomial a difference of squares?
9a2 - 8b2

A) Yes B) No

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Solution Summary

Twenty-five basic algebra problems are solved.

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