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# factor, simplify and multiply

1. Factor: 48-16v+v^2

2. Simplify: 3 sq. rt -1/25

3. Simplify by factoring: sq rt 32a^2b

4. Multiply: (b+1/2)(b+1/4)

5. For the following equation, state the value of the discriminant and then describe the nature of the solution.

16x^2+5x+2=0

6. Factor completely: 144a^2+648ag+729g^2

7. Factor completely: 2x^7-12x^6+14x^5

8. Perform indicated operations and simplify: w-2/w-3 - w+1/w+3 + w-9/w^2-9

9. Identify the degree of each term of the polynomial and the degree of the polynomial.

-9x^3 + 4x^2 + 5x + 8

10. Add. Simplify if possible: 9v/v^2-25 + v/v-5

11. Solve: 15x^4 - 13x^2 + 2 = 0

12. Subtract. Simplify by collecting like radical terms if possible.

5sq rt 32 - 2sq rt 2

13. Solve: 2x^2 = 10; find the x-intercept of f(x) = 2x^2 = 10

14. Subtract polynomials: (-8w^2 + 4w + 2) - (8w^2 + 2)

15. Multiply: (5x + 6)*(3x^2 + 3x +1)

16. Add:

(4s^4 - 3s^3 + 4s^2 + 12s -10) + (s^5 + 9s^3 +3s^2 - 4s + 6) + (-7s^4 + s^2 - 4s - 8)

17. Use rational exponents to write x^1/7 * y^1/5 * z^1/2 as a single radical expression.

18. Rewrite the following expression with positive exponents: (45xy)^-5/8

19. Solve: b2 - 4b - 32 = 0
20. Divide and simplify: z^5/z^19

21. Use rational exponents to simplify: ^3sq rt x^15

22. Solve: 8/v = 9/v - 1/5

23. Multiply and simplify: 25y^2/4y^2 - 8y + 4 * 4y-4/5y

24. Multiply and simplify. Assume variables represent nonzero real numbers.

x^15 * X^0

25. Factor completely: 81b^2 + 16 + 72b

26. Find the greatest common factor for the group of terms.

-66a^2, 11a^5

27. Use the quadratic formula to solve the equation: 2x^2 - 5x = -10

28. Solve: x^2 + 14x + 4 = 0

29. Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function.

f(x) = ½ (x+9)^2 + 4

30. Find the x-intercept for the graph of the equation: y = x^2 + 4x - 5

#### Solution Preview

Hi,

Please see attached for the solution to the given problems.

Hope this helps you in your studies.

Best regards,

1. Factor: 48-16v+v^2

Solution:

2. Simplify: 3 sq. rt -1/25

Solution:

3. Simplify by factoring: sq rt 32a^2b

Solution:

4. Multiply: (b+1/2)(b+1/4)

Solution:

5. For the following equation, state the value of the discriminant and then describe the nature of the solution.

16x^2+5x+2=0

Solution:

= 2 complex roots

6. Factor completely: 144a^2+648ag+729g^2

Solution:

7. Factor completely: 2x^7-12x^6+14x^5

Solution:

8. Perform indicated operations ...

#### Solution Summary

The expert factors, simplifies and multiplies functions. This posting contains the solution to the given problems.

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