Question : The factors of $x^2+4 y^2+4 y-4 x y-2 x-8$ are:

Option 1: $(x-2 y-4)(x-2 y+2)$

Option 2: $\left(x^2-2 y-4\right)\left(x^2-2 y+2\right)$

Option 3: $(x+2 y-4)(x+2 y+2)$

Option 4: $\left(x^2-2 y-4\right)\left(x^2+2 y+2\right)$

Question : What is the LCM of $\left(8 x^3+80 x^2+200 x\right)$ and $\left(4 x^4+16 x^3-20 x^2\right)$?

Option 1: $8 x^2(x+5)^2(x-1)$

Option 2: $8 x^2(x-1)^2(x+5)$

Option 3: $4 x^2(x-1)^2(x+5)$

Option 4: $4 x^2(x+5)^2(x-1)$

Question : Expand and simplify the algebraic expression:
$(x-5)^2+(x+3)^2+4x$

Option 1: $2\left(x^2-17\right)$

Option 2: $2\left(x^2+17\right)$

Option 3: $\left(x^2+17\right)$

Option 4: $2\left(x^2-5 x+17\right)$

Question : Simplify the following equation. What is the difference between the two values of $x$?
$7 x+4\left\{x^2 \div(5 x \div 10)\right\}-3\left\{5 \frac{1}{3}-x^3 \div\left(3 x^2 \div x\right)\right\}=0$

Option 1: 8

Option 2: 16

Option 3: 5

Option 4: 17

Question : If $2x+\frac{1}{2x}=2,$ what is the value of $\sqrt{2\left (\frac{1}{x}\right)^{4}+\left (\frac{1}{x}\right)^{5}}\; ?$

Option 1: 1

Option 2: 2

Option 3: 4

Option 4: 8