Advanced Math: Equivalent expressions — Quiz 4

Questions in this quiz (10)

1. Which of the following is equivalent to $$(a+\frac{c}{3})^2$$?

   • $$a^2+\frac{c^2}{3}$$
   • $$a^2+\frac{2ac}{3}+\frac{c^2}{9}$$
   • $$a^2+ac+\frac{c^2}{9}$$
   • $$a^2+\frac{ac}{3}+\frac{c^2}{3}$$

2. If $$b=m+n$$, which of the following is equivalent to $$x^2-m^2-2mn-n^2$$?

   • $$(x+b)^2$$
   • $$(x-b)^2$$
   • $$(x+b)(x-b)$$
   • $$x^2-bx-b^2$$

3. $$(\frac{2}{3}x+4)-(\frac{1}{2}x-6)$$ Which of the following is equivalent to the expression above?

   • $$\frac{1}{6}x+10$$
   • $$\frac{1}{6}x-2$$
   • $$-\frac{5}{6}x+10$$
   • $$-\frac{1}{6}x-2$$

4. If $$k-x$$ is a factor of $$-x^2+\frac{1}{16}nk^2$$, where $$k$$>$$0$$, what is the value of $$n$$?

   • $$-16$$
   • $$-1$$
   • $$1$$
   • $$16$$

5. Which expression is equivalent to $$(x^2+7)^2+(x-3)(x+3)$$?

   • $$x^4+14x^2+46$$
   • $$x^4+15x^2+40$$
   • $$x^4+13x^2+40$$
   • $$x^4+14x^2+40$$

6. One of the factors of $$x^3+18x^2+81x$$ is $$x+b,$$ where $$b$$ is a positive constant. What is the smallest possible value of $$b?$$

   • $$3$$
   • $$6$$
   • $$9$$
   • $$8$$

7. If $$x^2=p+q$$ and $$y^2=p+r$$, which of the following is equal to $$(x^2-y^2)^2$$?

   • $$q^2-2qr+r^2$$
   • $$p^2-2pr+r^2$$
   • $$q^2+2qr+r^2$$
   • $$p^2-2pq+q^2$$

8. The expression $$6x^2+bx-20$$ can be written as $$(mx+n)(px+q)$$, where $$m$$, $$n$$, $$p$$, and $$q$$ are integers. Which of the following must be an integer?

   • $$\frac{b}{m}$$
   • $$\frac{b}{n}$$
   • $$\frac{20}{m}$$
   • $$\frac{20}{n}$$

9. $$9a^2+30ab+25b^2$$ Which of the following is a factor of the polynomial above?

   • $$3a+b$$
   • $$3a+5b$$
   • $$9a+5b$$
   • $$3a+25b$$

10. $$(3x+2)^2-(x-4)+3(x+1)$$ Which of the following is equivalent to the expression above?

    • $$9x^2+14x+11$$
    • $$9x^2+16x+11$$
    • $$9x^2+14x+13$$
    • $$9x^2+16x+13$$