Factorization & Simplification — Quiz 3

Questions in this quiz (10)

1. What is $$\frac{2! + 3!}{4! + 5!}$$ in simplified form?

   • $$\frac{1}{18}$$
   • $$\frac{1}{48}$$
   • $$\frac{5}{9}$$
   • $$\frac{1}{60}$$

2. What is the completely factored form of $$x^4 - 81$$ over the reals?

   • $$(x - 3)(x + 3)(x^2 + 9)$$
   • $$(x - 3)^2(x + 3)^2$$
   • $$(x - 3)^2(x^2 + 9)$$
   • $$(x - 9)(x + 9)(x^2 + 9)$$

3. Which of these is the completely factored form of $$27x^3 + 64$$ over the reals?

   • $$(3x - 4)(9x^2 - 12x + 16)$$
   • $$(3x + 4)(9x^2 - 12x + 16)$$
   • $$(3x + 4)(9x^2 + 12x + 16)$$
   • $$(3x - 4)(9x^2 + 12x - 16)$$

4. Simplify the following expression: $$\frac{(3x^5y^2)(2x^3y^4)^2}{18x^9y^8}$$

   • $$\frac{x^2y^2}{6}$$
   • $$\frac{2x^2y^3}{3}$$
   • $$\frac{2x^2y^2}{3}$$
   • $$\frac{x^2y^2}{3}$$

5. Simplify the expression: $$y(5+y)-4(y^2+5y-3)$$

   • $$-3y^2+15y-12$$
   • $$-3y^2+15y+12$$
   • $$3y^2-15y+12$$
   • $$-3y^2-15y+12$$

6. Simplify the following algebraic expression: $$\frac{x^2-25}{x^3-2x^2-15x}$$

   • $$\frac{x+5}{x-3}$$
   • $$\frac{x+5}{x+3}$$
   • $$\frac{x+5}{x^2+5x}$$
   • $$\frac{x+5}{x(x+3)}$$

7. For all real numbers $$z$$, what is $$|-z|+|z|$$?

   • $$2|z|$$
   • $$-2z$$
   • $$0$$
   • $$2z$$

8. Which of the following is a simplified form of $$\sqrt{98}-\sqrt{18}$$?

   • $$4\sqrt{2}$$
   • $$5\sqrt{2}$$
   • $$-2\sqrt{2}$$
   • $$\sqrt{80}$$

9. Which of the following fractions is equal to: $$\frac{1}{2^{10}} - \frac{1}{2^{11}}$$?

   • $$\frac{1}{2}$$
   • $$-\frac{1}{2}$$
   • $$\frac{1}{2^{11}}$$
   • $$\frac{1}{2^{-1}}$$

10. If $$c$$ > $$0$$ and $$d$$ > $$0$$, what does $$2 \cdot (c^0 + d^0)^3$$ equal?

    • 16
    • 8
    • 0
    • 2