Question 1 :
Find the value of $k$, if $x-1$ is a factor of $p(x)$ in the following cases:$p(x)=kx^2-\sqrt 2x+1$<br/>
Question 3 :
What must be added to $x^3-3x^2-12x + 19$, so that the result is exactly divisible by $x^2 + x-6$?
Question 5 :
If $a + b+ c = 0$ , then $\dfrac{(b + c)^2}{3bc} + \dfrac{(c+a)^2}{3ac} + \dfrac{(a + b)^2}{3ab} $ is 
Question 6 :
The coefficient of $x$ in the expansion of $(x + 3)^3$ is
Question 7 :
Simplify: $(x - 3y - 5z)(x^2 + 9y^2 + 25z^2 + 3xy - 15yz + 5zx)$
Question 8 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.
Question 10 :
If the polynomial $3x^4-4x^3-3x-1$ is divided by $x-1$, then the remainder is :
Question 11 :
If $(x-1)$ and $(x-2)$ are factors of $x^4-(p-3)x^3-(3p-5)x^2+(2p-9)x+6$ then the value of $p$ is:
Question 13 :
Factorise : ${ (ax+by) }^{ 2 }+{ (2bx-2ay) }^{ 2 }-6abxy$
Question 15 :
Find the quotient $q(x)$ and remainder $r(x)$ of the following when $f(x)$ is divided by $g(x)$.<br/>$p(x)=x^3-3x^2-x+3$;<br/>$g(x)=x^2-4x+3$<br/>
Question 16 :
When $p (x)$ is divided by $ax - b$ then the remainder is :<br>
Question 17 :
On dividing $f(x)=2x^5+3x^4+4x^3+4x^2+3x+2$ by a polynomial $g(x)$, where $g(x)=x^3+x^2+x+1$, the quotient obtained as $2x^2+x+1$. Find the remainder $r(x)$.<br/>
Question 18 :
Divide the following and write your answer in lowest terms: $\dfrac{3x^2-x-4}{9x^2-16}\div \dfrac {4x^2-4}{3x^2-2x-1}$
Question 19 :
Workout the following divisions<br/>$54lmn (l + m) (m + n) (n + 1) \div 81mn (l + m) (n + l)$
Question 20 :
If $a\, +\, \displaystyle \frac{1}{a}\, =\, m$ and $a\, \neq\, 0$, find in terms of 'm' the value of $a\, -\, \displaystyle \frac{1}{a}$ .
