0. Review of Algebra

In Exercises 65–92, factor completely, or state that the polynomial is prime. 9x³−9x

Factor each polynomial. See Examples 5 and 6. 27-r³

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 2x^2+5x−3

Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [(y² +2)⁵(3y) - y³(6)(y²+2)⁴(3y)] / [(y²+2)⁷]

Simplify each complex fraction. $\(\frac{\frac{6}{x^2 - 25}\) + x}{\(\frac{1}{x - 5}\)}$

Simplify each complex fraction. [ 1/(a³+b³) ] / [ 1/(a² + 2ab + b²) ]

In Exercises 65–92, factor completely, or state that the polynomial is prime. 2x⁴−162

Factor each polynomial. See Example 7. $10m^4+43m^2-9$

Factor each trinomial, if possible. See Examples 3 and 4. 14m²+11mr-15r²

Factor completely: $x^3+x^2-4x-4.$

Factor by any method. See Examples 1–7. x²+xy-5x-5y

Write each rational expression in lowest terms. 8k + 16 / 9k + 18

In Exercises 57–64, factor using the formula for the sum or difference of two cubes. 8x^3+125