Factoring and Solving Equations and Inequalities
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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.
(√[45xy^17)/(√[5xy])
8. Simplify the radical expression . Assume that all variables represent positive numbers.
√[275y^15b^11]
9. Simplify and combine like radicals
√[18] - √[50] + √[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)
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