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 : The factors of $ x^4+x^2+25$ are:

Option 1:  $\left(x^2+3 x-5\right)\left(x^2-3 x+5\right)$

Option 2: $\left(x^2+3 x+5\right)\left(x^2-3 x+5\right)$

Option 3: $\left(x^2-3 x+5\right)\left(x^2-3 x+5\right)$

Option 4: $\left(x^2+3 x+5\right)\left(x^2+3 x+5\right)$

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 $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:

Option 1: $\frac{9}{4}$

Option 2: $\frac{27}{8}$

Option 3: $\frac{5}{2}$

Option 4: $2$

Question : Simplify the following:
$\frac{\cos x-\sqrt{3} \sin x}{2}$

Option 1: $\cos \left(\frac{\pi}{3}-x\right)$

Option 2: $\sin \left(\frac{\pi}{3}+x\right)$

Option 3: $\cos \left(\frac{\pi}{3}+x\right)$

Option 4: $\sin \left(\frac{\pi}{3}-x\right)$