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# Factoring and Solving Equations and Inequalities

1. Factor the polynomial 88 x^6 y^6 + 16 x^3 y^4 - 8 x^5 y^3, if possible.

2. Factor 5 x^2 + 5 x y + 8 x + 8 y by grouping.

3. Factor the polynomial.

256 a^4 - 81 b^4

4. Solve the equation.

x 2 + 11 x + 30 = 0

5. Do the operations and simplify.

(x^2 + 4x + 4)/(x) . (x^2 - 2x)/(x^2 - 4)

6. Simplify the expression

(x^2 + 6x - 7)/(4x^2 + 7x + 3) . (16x^2 - 9)/(4x^2 + 25x - 21)

7. Simplify the radical: . Assume that all variables represent positive numbers.

(&#8730;[45xy^17)/(&#8730;[5xy])

8. Simplify the radical expression . Assume that all variables represent positive numbers.

&#8730;[275y^15b^11]

9. Simplify and combine like radicals

&#8730;[18] - &#8730;[50] + &#8730;[98]

10. Use the quadratic formula to solve the following equation.

5 x + 6 = 14 x 2

11. Factor the trinomial. Factor out all common monomials first.

21x^3 - 52x^2 + 32x

12. Solve the equation.

x/8 = 13

13. Solve the equation.

b/3 - b/4 = 5

14. What is the slope of the line passing through the points ( 7, 2 ) and ( 0, 0 )?

15. Solve the inequality.

-4/17 < - 8/17x

16. Find the product.

- 2x (3x^2 - 5x + 8)

#### Solution Summary

Factoring and Solving Equations and Inequalities are investigated. 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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