0. Review of Algebra

A rigid bar (negligible mass) of length 80 cm connects a large sphere with a mass (m₁) of 25 g to a small sphere with an unknown mass (m₂). The large sphere is located at one end of the bar, with the center of mass of the bar located 22 cm away from this sphere. Determine the mass of the sphere (in grams) at the other end of the bar.

In Exercises 93–102, factor and simplify each algebraic expression. (x+3)^1/2−(x+3)^3/2

Factor by any method. See Examples 1–7. $(2y-1{)}^2-4(2y-1)+4$

Factor out the greatest common factor from each polynomial. See Example 1. 8k³+24k

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 9x²+5x−4

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.) [(x² +1)⁴(2x) - x²(4)(x²+1)³(2x)] / [(x²+1)⁸]

Factor out the greatest common factor from each polynomial. See Example 1. 6x(a+b)-4y(a+b)

Work each problem. Match each polynomial in Column I with its factored form in Column II.

Factor the polynomial by grouping

$-x^2-5x+7x+35$