Question 1 :
State whether the following statement  is true or false.$(x-1)$ is a factor of ${x}^{3}-27{x}^{2}+8x$.
Question 2 :
If $a\, -\displaystyle \frac{1}{a}\, =\, 8$ and $a\, \neq\, 0$; find $a^{2}\, -\, \displaystyle \frac{1}{a^{2}}$
Question 5 :
If (x -1) is a factor of polynomial f(x) but not of g(x), then it must be a factor of
Question 7 :
Use the product $ (a+b)(a-b) = a^2-b^2$ to evaluate:<br>$21\times 19 $
Question 8 :
Use factor theorem to verify that the following polynomial q(x) is a factor of p(x) $p(x)=x^5-x^4-4x^2-2x+4, \ q(x)=x-2$<br/>
Question 9 :
If quotient = $3x^2\, -\, 2x\, +\, 1$, remainder = $2x - 5$ and divisor  = $x + 2$, then the dividend is:
Question 10 :
The remainder when $x^{6} - 3x^{5} + 2x^{2} + 8$ is divided by $x - 3$ is<br>
Question 11 :
The sum of two numbers is 9 and their product is 20. Find the sum of their cubes<br/>
Question 12 :
If $P=\dfrac {{x}^{2}-36}{{x}^{2}-49}$ and $Q=\dfrac {x+6}{x+7}$ then the value of $\dfrac {P}{Q}$ is:
Question 13 :
Factorise : $(a - b)^3 + (b - c)^3 + (c - a)^3$
Question 14 :
If $\displaystyle  a^{2}+b^{2}=13 \ and \ ab=6 $ find :<br/>$\displaystyle  3\left ( a+b \right )^{2}-2\left ( a-b \right )^{2}$<br/>
Question 15 :
If $\displaystyle  a^{2}+b^{2}=13 \ and \ ab=6 $ find :<br/>$\displaystyle  a^{2}-b^{2}$<br/>
Question 16 :
If $ a^2+b^2=29 $ and $ ab=10 $, then find $ a-b $. 
Question 17 :
The value of (a - b)(a$^2$ + ab + b$^2$) is
Question 19 :
State whether True or False, if the following are zeros of the polynomial, indicated against them:<br/>$p(x)=x^2-1, \ x=1, -1$<br/>
Question 20 :
If the polynomial $x^3-x^2+x-1$ is divided by $x-1$, then the quotient is :
Question 21 :
If one factor of the expression $x^{3} + 7kx^{2}-4kx+12$ is $(x+3)$, then the value of $k$ is<br/>
Question 22 :
If on division of a polynomial p (x) by a polynomial g (x), the quotient is zero, what is the relation between the degrees of p (x) and g (x) ?<br/>
Question 23 :
Without actually calculating the cubes, find the value of :$\left ( \dfrac{1}{2} \right )^{3}+\left ( \dfrac{1}{3} \right )^{3}-\left ( \dfrac{5}{6} \right )^{3}$<br/>
Question 27 :
Simplify: $(x - 3y - 5z)(x^2 + 9y^2 + 25z^2 + 3xy - 15yz + 5zx)$
Question 28 :
<b></b>If $ a^2+b^2=10 $ and $ ab=3 $, then find $ a+b $. 
Question 29 :
Use the identity $(x + a) (x + b) = x^2 + (a + b) x + ab$ to find the following products.$(xyz +4) (xyz +2)$
Question 30 :
Verify whether the following are zeros of the polynomial indicated against them:<br/>
Question 31 :
State whether the given statement is true or false:Zero of $q(x) = 2x - 7$ is  $x=\cfrac{7}{2}$<br/>
Question 32 :
Find out whether or not the first polynomial is a factor of the second polynomial:$4a-1, 12a^2-7a-2$
Question 33 :
Find the remainder when $10x-4x^{2}-3$ is divided by $x+2$ using remainder theorem.
Question 35 :
If one zero of a quadratic polynomial $x^2+3x+k$ is $2$. Find the value of $k$.
Question 38 :
Choose the correct answer from the alternatives given.<br/>If x - $\dfrac{1}{x}$ = 3 then find the value of $x^3 + \dfrac{1}{x^3}$. 
Question 40 :
If 1 is zero of the polynomial p(x) = $\displaystyle ax^{2}-3\left ( a-1 \right )x-1$ then the value of 'a' is
Question 41 :
Find the remainder when $x^{3} + 3x^{2} + 3x + 1$ is divided by $x - \dfrac {1}{2}$.
Question 44 :
Without actually calculating the cubes, find the value of each of the following:$(28)^3+(-15)^3+(-13)^3$<br/>
Question 45 :
State whether True or False, if the following are zeros of the polynomial, indicated against them:$p(x)=lx+m, \ x=-\dfrac {m}{l}$<br/>
Question 46 :
The value of $m$, in order that ${ x }^{ 2 }-mx-2$ is the quotient when $3{ x }^{ 3 }+3{ x }^{ 2 }-4$ is divided by $x+2$, is
Question 48 :
One factor of $x^4 + x^2-20$ is $x^2+ 5$. The other factor is
Question 49 :
State whether True or False.Divide: $x^6-8   $ by $  x^2-2$, then the answer is $x^4+2x^2+4$.<br/>
Question 50 :
The roots of $x(x^2 + 8x + 16)(4 - x ) = 0$ are