0. Review of Algebra

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]

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.) [4(x²- 1)³ + 8x(x²-1)⁴] / [16(x²-1)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.) [10(4x²-9)² - 25x(4x²-9)³] / [15(4x²-9)⁶]

In Exercises 91–100, find all values of x satisfying the given conditions. $y=x^3+4x^2-x+6$ and $y=10$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $4x^3-12x^2=9x-27$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $4y^3-2=y-8y^2$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $5x^4-20x^2=0$

Solve each equation in Exercises 96–102 by the method of your choice. x^3 + 2x^2 = 9x + 18

Factor completely, or state that the polynomial is prime. 3x^4-12x^2

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

Factor completely, or state that the polynomial is prime. 16x^2-40x+25

In Exercises 1–10, factor out the greatest common factor. x²(2x+5)+17(2x+5)

In Exercises 1–10, factor out the greatest common factor. x(2x+1)+4(2x+1)

In Exercises 49–56, factor each perfect square trinomial. x^2−14x+49

In Exercises 49–56, factor each perfect square trinomial. 4x^2+4x+1