Equivalent Expressions 2 — Advanced Math

Questions in this quiz (8)

1. The expression $$(3600+40x^2)+5(60x^2-200)$$ can be written in the form $$ax^2+b$$, where $$a$$ and $$b$$ are constants. What is the value of $$a+b$$?

   • $$2800$$
   • $$2940$$
   • $$3400$$
   • $$3600$$

2. $$\frac{8x^2+18x+9}{4x^2+11x-6}$$Which of the following is equivalent to the expression below?

   • $$\frac{(4x+3)}{(x+3)}$$
   • $$\frac{(2x+3)}{(4x-1)}$$
   • $$\frac{(x+3)}{(4x+3)(x-1)}$$
   • $$\frac{(2x+3)(4x+3)}{(x+3)(4x-1)}$$

3. Which expression is equivalent to $$t^2-4t-45$$?

   • $$(t-9)(t+5)$$
   • $$(t-5)(t+9)$$
   • $$(t+9)(t+5)$$
   • $$(t-9)(t-5)$$

4. $$4x^2+20xy+25y^2$$Which of the following is a factor of the polynomial above?

   • $$2x+5y$$
   • $$2x+25y$$
   • $$4x+5y$$
   • $$4x+25y$$

5. Which of the following is equivalent to the expression $$x^4-9x^2-36$$?

   • $$(x^2+3)(x^2-12)$$
   • $$(x^2+4)(x^2-9)$$
   • $$(x^2+6)(x^2-6)$$
   • $$(x^2+12)(x^2-3)$$

6. The expression $$3\sqrt[4]{16z^{12}}\cdot\sqrt[6]{64z^{9}}$$ is equivalent to $$cz^d$$, where $$c$$ and $$d$$ are positive constants and $$z$$ > $$1$$. What is the value of $$c+d$$?

   • $$12$$
   • $$\frac{9}{2}$$
   • $$\frac{33}{2}$$
   • $$33$$

7. The expression $$8x^2+cx-18$$, where $$c$$ is a constant, can be rewritten as $$(hx+k)(vx+j)$$, where $$h$$, $$k$$, and $$j$$ are integer constants. Which of the following must be an integer?

   • $$11$$
   • $$13$$
   • $$17$$
   • $$19$$

8. The expression $$8x^2+cx-18$$, where $$c$$ is a constant, can be rewritten as $$(hx+k)(vx+j)$$, where $$h$$, $$k$$, and $$j$$ are integer constants. Which of the following must be an integer?

   • $$\frac{c}{h}$$
   • $$\frac{c}{k}$$
   • $$\frac{18}{h}$$
   • $$\frac{18}{k}$$