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Question 4 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$a^2-b^2 ; a-b$

Question 5 :
Divide:$\left ( 15y^{4}- 16y^{3} + 9y^{2} - \cfrac{1}{3}y - \cfrac{50}{9} \right )$ by $(3y-2)$Answer: $5y^{3} + 2y^{2} - \cfrac{13}{3}y + \cfrac{25}{9}$

Question 6 :
Assertion: If $ p x^{2}+q x+r=0 $ is a quadratic equation $ (p, q, r \in R $ ) such that its roots are $ \alpha, \beta $ and $ p+q+r<0, p-q +r<0 $ and $ r>0, $ then $ [\alpha]+[\beta]=-1, $ where [.] denotes greatest integer function. Reason: If for any two real numbers $ a $ and $ b $, function $ f(x) $ is such that $ f(a) f(b)<0 \Rightarrow f(x) $ has at least one real root lying in $ (a, b) $

Question 8 :
If $ \alpha, \beta $&#160;be the roots of the equation $&#160;a x^{2}+b x+c=0, $&#160;then value of $\dfrac{ \left(a \alpha^{2}+c\right) }{(a \alpha+b)}+\dfrac{\left(a \beta^{2}+c\right)}{ (a \beta+b)} $&#160;is

Question 9 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to